There are few things more dialectically riveting in the theater than a great musical actor standing downstage-center, in the demarcating glow of a spotlight, and singing her heart out. It’s a spectacle at once intimate and grandly histrionic, advancing the plot and removed from it. The character shares her innermost thoughts; the actor radiantly shows off her chops. The female leads in two Broadway revivals are blazing through such numbers eight times a week these days, both in unorthodox takes: Jessie Mueller as Julie Jordan in Carousel and Lauren Ambrose as Eliza Doolittle in My Fair Lady.

A certain critical consternation awaited these productions, with good reason. Here, as several commentators have noted, are shows (along with the upcoming Pretty Woman and next season’s Kiss Me Kate), written by men and directed by men and based on source material mostly by men, whose female protagonists can seem to succumb cheerily to being beaten, bullied, rescued, or tamed by their male counterparts. A measure of these times of debate over what to do with historical expressions that now seem dishonorable, the revivals of Carousel (Rodgers and Hammerstein, 1945) and My Fair Lady (Lerner and Loewe, 1956) opened in mid-April, the same week that New York City, in response to protests, removed a statue from Central Park of one J. Marion Sims, a 19th-century surgeon who operated on female slaves without anesthesia or consent. Should sexist old shows—notwithstanding charms like Carousel’s soaring score or My Fair Lady’s high entertainment quotient—meet a similar fate? Should they be knocked from the repertoire?

Not necessarily. Theater is made of flesh and voice, not of marble or bronze, and when live human beings embody theatrical roles, they bring perspectives, quirks, critiques, and sheer virtuosity that can contribute to contesting a show’s hoary elements. And there’s no great risk in trying. Unlike a statue, a play can’t be smashed irretrievably to smithereens. Even the clumsiest staging or most boneheaded interpretation cannot define a show; someone else can come along and make another production.

Artists and scholars have been thinking about how to grapple with the apparent misogyny in the masterful midcentury musicals since long before me too became a hashtag. Meanwhile, the tight licensing grip that creators (or their estates) have long maintained, demanding absolute fidelity to the original stage versions of their works, has started to loosen, allowing—to cite just a few examples—a female Bobbi in Marianne Elliott’s upcoming London production of Company; new choreography by Hofesh Shechter for the most recent Broadway revival, in 2015, of Fiddler on the Roof; and same-sex couples as the parallel romantic pairs in Bill Rauch’s version of Oklahoma! at the Oregon Shakespeare Festival. So the questions for the “golden age” musicals now on Broadway—as for any production, anywhere—must be: Why now? And, especially, how now?

In the case of My Fair Lady, the remarkable center-stage number comes in the latter half of the first act. After being worked to the brink of exhaustion, Eliza Doolittle successfully pronounces some phrases without her Cockney accent leaking through. “The rain in Spain stays mainly in the plain,” she manages to say, and the line lilts into a refrain for a celebratory tango she slides through with her taskmaster, the linguist Henry Higgins (a droll and driven Harry Hadden-Paton), who has bet that within six months, he can pass off the poor, unwashed, undereducated flower girl as a duchess at an embassy ball. When Higgins and his kindly colleague Colonel Pickering (Allan Corduner) retreat happily for the night, Eliza, too keyed up for sleep, cradles her books and, giddy at her own achievement, sings “I Could Have Danced All Night” with a full-out abandon we haven’t heard from her until this point. Though it is often treated as a song suggesting that Eliza is falling in love with Higgins, here Ambrose plays “I Could Have Danced” more for the sense of self-discovery, which is really what impels it: “I could have spread my wings / And done a thousand things / I’ve never done before.”

Director Bartlett Sher has staged something extraordinary here. Toward the end of the song, he has Ambrose walk out of Higgins’s lavish two-story study—with its floor-to-ceiling bookshelves, Oriental rugs, and oh-so-progressive Kandinsky-like painting on the wall—straight through its fourth wall toward the lip of the stage; meanwhile, the study (the set is designed by Michael Yeargan) glides upstage into the deep, dark expanse of Lincoln Center’s Vivian Beaumont Theater. Eliza stands alone on the vast stage, bursting with song and newly found confidence. Sher hasn’t changed the script, and yet this subtle bit of staging is emotionally seismic. Eliza finds her voice by singing. Hear her roar.

In general, Sher’s production revolves around Eliza’s process of coming into her own, but never in an overblown, unsupported way (not even in the innovative, heart-quickening ending, which I won’t divulge here). This, after all, is the arc of the show itself, no matter how often it’s thought of as a love story. True, the transformation is mutual: Eliza has just as much impact on her priggish, chauvinistic tutor as he has on her, and Hadden-Paton delivers Henry’s own musical inner monologue, “I’ve Grown Accustomed to Her Face,” with a touching sense of bewilderment over the unfamiliar rise of sentiment in his heart.

But—and weeks after a self-identified incel, or “involuntary celibate,” drove a van into a crowd, killing mostly women, in Toronto, this, lamentably, still needs to be said—just because Higgins discovers some affection for Eliza, that does not mean she has any obligation to reciprocate it. Especially not after his persistent belittling and name-calling. He refers to Eliza as his property; calls her “baggage,” a “squashed cabbage leaf,” a “presumptuous insect,” a “draggletailed guttersnipe,” and more; and sings not one but two misogynistic manifestos (“A Hymn to Him” and “I’m an Ordinary Man”). Hadden-Paton’s performance is nimble enough to turn the professor’s obtuseness about his own entitlement and white-guy fragility into comic irony, but Eliza’s musical riposte stands as the show’s general attitude: “There’ll be spring ev’ry year without you / England still will be here without you…. / Without your pushing them, the clouds roll by / If they can do without you, ducky, so can I!”

The source for My Fair Lady—George Bernard Shaw’s play Pygmalion (along with the screenplay for the 1938 film version)—makes the case for Eliza’s independence even more strongly, and Sher and company have clearly returned to it for guidance. Shaw was so annoyed by the romantic reading that Herbert Beerbohm Tree gave to Higgins in Pygmalion’s first London production in 1914—“I writhed in hell” watching it, Shaw wrote—that the playwright appended a sort of fan-fiction scenario to the drama, in which he describes what might happen to Eliza after the action of Pygmalion ends: that she would emphatically not marry Higgins, but rather just remain his friend.

Of course, Shaw was as interested in class as in gender—Eliza is an intersectional hero!—and the musical adaptation carries over his mockery of bourgeois hypocrisy and his critique of capitalist inequity. When she was in Covent Garden, Eliza tells Higgins, who has commented that marriage is her best option for the future, “I sold flowers. I didn’t sell myself. Now you’ve made a lady of me, I’m not fit to sell anything else.”

Sher and his team underline the class/gender nexus throughout the play, most efficiently and hilariously in a bit of business during the scene at the races—Eliza’s first effort to pass in public as a lady. The crowd of wealthy spectators, dressed in sumptuous, creamy pearls and mauves with sleek Edwardian contours (the costume designer is Catherine Zuber), moves in tidy lines and upright postures. When Eliza enters in her own shiny narrow dress and is offered a seat, she finds that she can’t fully bend her knees and has to gingerly settle herself sideways. In contrast, Eliza’s father, Alfred (a spirited Norbert Leo Butz), and his drinking buddies sprawl and stagger in his scenes outside a pub, and when Alfred comes into lots of money (long story), he rues his ascent into “middle-class morality,” not least the expectation that he wed his partner. Into a raucously staged “Get Me to the Church on Time,” Sher first brings out a line of can-canning dance-hall women, then of can-canning men wearing the same sort of flouncy red skirts, and then a mock marriage procession featuring a cross-dressed couple; the assembled carry a prone Alfred aloft, as if to his own funeral.

Apart from the pleasures of its exuberant theatricality, the mayhem suggests an alternative world beyond the constraining options to which Eliza has been exposed. And so does a column of white-clad women—suffragists with sashes and signs demanding “Votes for Women”—who silently cross the stage in a couple of crowd scenes. My Fair Lady originally premiered at a time when American popular culture was promoting a perkily domesticated image of white, middle-class femininity (soon after the show opened, images of June Cleaver vacuuming in pearls became a familiar sight on living-room TVs across America), and it became a colossal hit, running on Broadway for more than six years. Today, without radically altering the show, Sher lets us feel the same exhilaration that Eliza discovers when she risks giving up her comfort for her self-sovereignty.

In Carousel, a show that’s not as given to disruption as My Fair Lady has been from the start, it’s much harder to challenge the genre’s gender conventions—nor does director Jack O’Brien seem to have been much interested in trying. Set in late-19th-century Maine, Carousel tells the troubling story of a rough-hewn carnival barker, Billy Bigelow (Joshua Henry), and the quiet but headstrong mill worker, Julie Jordan (Jessie Mueller), whom he marries. With the exception of one brief and shining moment—when Mueller sings right out to the audience—this is a standard-issue Carousel, albeit one featuring a first-rate cast and a full pit orchestra. The production’s primary (and substantial) pleasure is in its ardent delivery of the resplendent score. If you don’t get chills when Mueller and Henry, both strong, emotional singers, convey the reluctant siege of their romance in the duet “If I Loved You,” and if you aren’t thoroughly beguiled by Lindsay Mendez’s ebullient rendering, as Julie’s friend Carrie, of “(When I Marry) Mister Snow,” check your pulse.

And yet. Never mind a clunky choral scene or two (“This Was a Real Nice Clambake” is as inert as cold fish)—the show’s central arc needs fresh framing if a contemporary audience is to engage with it wholeheartedly. The difficulty isn’t only that Billy hits his wife and that she rationalizes his violence in dialogue (“He’s unhappy”) and in a cringe-inducing song (“Oh, what’s the use of wond’rin’ / If he’s good or if he’s bad? / He’s your feller and you love him / That’s all there is to that”). We know, alas, that such dynamics persist in abusive relationships. The deeper problem is that the show itself seems to rationalize the abuse as a function of Billy’s frustration—his failure to find work after being fired, in the first scene, from his post as a carousel barker, and his inability to fit in with Julie’s community.

Though Carrie encourages Julie to leave Billy after he hits her, the very structure of the show counteracts this possibility. As in other Rodgers and Hammerstein musicals (and many they influenced), there’s an implicit comparison between a main couple and their foils (here, Carrie and the fisherman Mr. Snow). As a character, Carrie may object to Billy’s violence, but as a structural parallel to Julie, she places her friend in an analogous position. “The first time he kissed me, the whiff of his clothes / Knocked me flat on the floor of the room,” Carrie sings to Julie. “But now that I love him, my heart’s in my nose / And fish is my fav’rite perfume.” The conventions of the musical prime the audience to expect Julie to stand by her man too, even if what knocks her flat on the floor is a slap.

How Julie might actually feel we have little chance to learn, and not only because, as Carrie puts it, she’s “as tight-lipped as an oyster.” Apart from “What’s the Use of Wond’rin’,” Julie doesn’t have any solo numbers. It’s Billy to whom Rodgers and Hammerstein gave a show-stopping, eight-minute opportunity to spill his heart—an event that brings the audience sympathetically close to an otherwise unlikable character—and it’s a tour de force for Henry, who performs it like a bouncing spring that suddenly tightens into a tenser and tenser coil. In that song, “Soliloquy,” which closes the first act, Billy reacts to news that Julie is pregnant. At first, he happily imagines a son, who will be “tall and as tough as a tree”; but then he panics: What if it’s a girl—“sweet and petite”—who will require his protection? That anxiety pushes him to seek money in a robbery, precipitating his death, and then his opportunity for redemption at the rear gates of Heaven.

Julie is left to mourn, but even before Billy’s death, she has little to do other than wring her hands over him—except at the show’s beginning. In the first two scenes, she pursues her desire for Billy with a forthrightness that shocks Carrie. (Mueller and Henry convey a sexual attraction that sends a charge clear to the back of the Imperial Theatre’s balcony.) Left alone along a pathway after Carrie rushes back to make the curfew at the mill workers’ barracks, Billy and Julie sing their stunning duet in what’s known as the “bench scene.”

Running about 12 minutes, the scene picks up strains of earlier melodies and uses underscoring to develop their relationship through a conversation in music. Because of these innovative techniques, Stephen Sondheim called the scene “probably the singular most important moment in the evolution of contemporary musicals.” In the most radical piece of staging in this production, O’Brien leaves them standing for most of the exchange (despite its name) and, most important, brings Mueller downstage to sing “If I loved you” not to Billy, but to the audience.

For a few stirring lines in the two-and-a-half-hour show, we are privy to Julie’s interior life as she imagines—in Mueller’s deeply grounded acting and beautiful singing—what loving Billy might mean. “Longin’ to tell you / But afraid and shy,” she sings, considering what would happen if she didn’t express her love: “I’d let my golden chances pass me by!” In that dialectical moment, as Julie searches her soul, Mueller transmitted passion and tenacity right into mine. And it made me wonder what golden chances the show itself let pass all of us by.