In all the discussion about the welcome if uneven revival of George Bernard Shaw’s Pygmalion, it seems to me that the genius of the play itself has been forgotten. Blame the musical.

Everyone of a certain theatergoing age is too familiar with Lerner and Loewe’s lovely, hummable score from My Fair Lady. It’s second nature to us now, like breathing out and breathing in. We can scarcely imagine Professor Higgins not singing “I’ve Grown Accustomed to Her Face,” Eliza Doolittle without “I Could Have Danced All Night” or her dad, Alfred P. Doolittle, the dustman, without his showstopping “I’m Getting Married in the Morning.” The 1956 musical version of Shaw’s rarely produced Pygmalion is so indelibly stamped on the imagination that you would be forgiven if you went to see the play and wondered, “Where’s the Ascot scene?”

The Roundabout Theater Company’s new production is the first major revival of Shaw’s great social comedy for more than 30 years, and for me the litmus test of any Pygmalion is how badly it makes us miss the musical. Alas, in this case the answer is too much.

Yet its British director, David Grindley, has honorably tried to remain true to the play, and the play—a masterly comic dissection not just of the British class system, but of capitalism as well—ought to be more than enough.

As Shaw commented, typically, after Pygmalion’s acclaimed premiere in 1913: “There must be something radically wrong with the play if it pleases everybody, but at the moment I cannot find what it is.”

THREE LEGENDS ARE involved here: Ovid’s tale of Pygmalion and Galatea; Shaw’s adaptation of it, which reversed Ovid’s happy ending; and the Lerner and Loewe musical, which reversed Shaw’s ending and had his Pygmalion, the irascible, middle-aged phonetician, and his Galatea, the young cockney flower girl who wants to be a lady, fall in love.

The musical is arguably among the best adaptations ever made of a great play, though in my view it didn’t “improve” it. In the compromised essentials, My Fair Lady has nothing to do with Shaw, and everything to do with Broadway.

Until his death in 1950, Shaw stubbornly refused all offers to turn Pygmalion into a musical. He knew in his bones that making a musical of this most British of plays would sentimentalize it, and he was right. Lerner and Loewe shrewdly gave the public what it really wanted by turning Pygmalion into a delightful Cinderella fairy tale, the kind equipped with what Shaw called “happy endings to misfit all stories.”

Yet the public in Shaw’s day had demanded a happy ending, too. (So did his leading actors.) The disgusted dramatist found such easy, popular sentiment “unbearable” and even rewrote the play’s original, ambiguous end to make it crystal clear that his unchangeable, eternally confirmed bachelor Henry Higgins isn’t in love with poor Eliza, and isn’t about to be in love with anyone under 45.

In the witty windbaggery of Shaw’s essay on the play, he went on to insist pedantically that Henry and Eliza, like more or less everyone else, simply aren’t suited to each other. He reiterates that she marries the kindly upper-class dope, Freddy Eynsford Hill.

Gawd! What a fate.

Eliza didn’t have a chance with Higgins. The best he can do is invite her to live with him and Colonel Pickering for the fun of it. “My idea of a lovable woman is someone as like you as possible,” he tells his mother alarmingly. “I shall never get into the way of seriously liking young women: Some habits lie too deep to be changed.”

The notion that these “habits” are the outcome of closeted homosexuality is somewhat simpleminded. Shaw’s plays aren’t about sex, but sexual politics, and Higgins, the spoiled mommy’s boy, is an Edwardian gentleman who simply prefers the clubby companionship of men. It doesn’t mean that he and a dear old bugger like Pickering are lovers. It means, as Higgins puts it decorously, that “women upset everything.”

For all his arrogant prejudice and presumption, Henry Higgins is no snob. He treats everyone rudely. An unlikely proponent of egalitarianism, he’s a proto-feminist in his own eccentric, insultingly lordly fashion. He ultimately wants Eliza to have the same freedom and independence he enjoys, and opposes the institution of marriage because he sees it as a compromising business deal. He’s Shaw’s mischievous symbol of freedom, just as his marvelously witty portrait of Eliza’s roguish dad—one of “the undeserving poor”—satirizes middle-class morality and represents the free spirit of conniving, opportunistic capitalism.

“Have you no morals, man?” Pickering asks him disapprovingly.

“Can’t afford them, governor,” comes his cheerful response.

Pygmalion contains more bite and intelligence than a mere romantic comedy set in an age, much like our own, of social-climbing “upstarts” who “give themselves away every time they open their mouths.”

I believe that Shaw wrote one of literature’s greatest romances by accident. Never trust what an artist says about his work, as the old saying goes—only what he does. Shaw’s strict opposition to sentimentalizing his dueling protagonists was sincere, but no man with a cold heart could have charmed the world by creating Eliza Doolittle.

BEWARE BRITS BEARING wits. David Grindley’s new production encourages Shawian laughter, yet it possesses little humor. Mr. Grindley has gone for Pygmalion’s darker message as if in steely opposition to the romance of the musical. But he belongs to the British school of directors that remains seriously faithful to Shaw in the way married couples display matching wedding rings. You note the good intentions, and recoil.

His Pygmalion barely suggests even the possibility of a romance between Eliza and Higgins. It lacks what Sam Goldwyn called “warmth and charmth.” Higgins must have the charmth, and Eliza the warmth.

Apart from a guest spot in The Vagina Monologues, Claire Danes, the film and TV actress, has scarcely appeared onstage before this, her Broadway debut, as Eliza. She does well (and her marquee name has sold an awful lot of tickets). But I’m afraid her performance is without a center. Ms. Danes has her moments, but as yet, she’s gamely impersonating Eliza in the same programmed way that Eliza impersonates a duchess. (The production has its own Higgins, the dialect coach Majella Hurley.)

Jefferson Mays—a Tony Award winner for his German transvestite in My Own Wife—has been encouraged to take Shaw’s description of Professor Higgins as “rather like an impetuous baby” far too literally. It’s true that Higgins, the puer aeternus, has two nannies (his housekeeper and his mother), but Mr. Mays mistakenly plays him as a big petulant baby throughout. He looks like a surprised pixie with a cute kiss curl in his hair. He always seems to be eating. (When it’s not chocolate, he’s munching an apple.) He’s hyperactive; he fidgets; he squirms; he bullies; he sulks; he all but sucks his thumb. His baby Higgins does everything a charmless child insists on doing. There’s fatally no affection in him.

“He remains likeable even in his least reasonable moments,” Shaw notes in the text about Higgins. Mr. Mays’ version is dislikable. Squabbling with the rebellious Eliza in the final act, he literally takes a swing at her and goes for her throat.

Shaw’s stage direction for this apparently murderous moment says only that he “turns on her so threateningly.” And it implicitly represents the emotional turning point of the play: Eliza has wounded Higgins, and pierced his heart.

I’ve sometimes criticized Broadway revivals for failing to take great plays seriously enough, but this time it’s different. Mr. Grindley’s overearnest production has failed to take Pygmalion lightly enough. It’s a high comedy, after all—the wittiest romance that G.B. Shaw never wrote.