And then there’s Valentina, an astrophysicist who, 40 years earlier, hooked up with Grampy when he visited the real world. The best thing to say about her is that she’s played by Faith Prince, looking game, if understandably confused.

In any case, Grampy and Valentina reunite when he returns to the real world to reclaim Betty, without whom the black-and-white world at home is fading. But will she go back with him, now that, with the help of her new friends, she is involved in a mayoral election, a sanitation scandal and a feminist quest to take charge of her identity?

I wish the show had taken charge of its identity too. Instead, one feels at all times the heavy hooves of a marketing imperative. The brand discipline is punishing; in David Rockwell’s scenic design, even the proscenium has spit curls.

And poor Trisha, hasn’t she lived through enough without being turned into a brand ambassador? “Betty Boop has been famous everywhere for like a hundred years!” she says, as one does. “Betty Boop is strong and smart and confident and capable.” She even gets a song, called “Portrait of Betty,” that hymns Boop’s praises as if she were, well, Eleanor Roosevelt: “She is not afraid to fight / For all the people who cannot defend themselves.” In short, as a typically well turned Birkenhead lyric puts it: “She has spunk, she has spine, she’s a saint, bottom line.”

And there it is. The bottom line.

Betty Boop, if not the earliest cartoons she appears in, is still under copyright protection. No doubt the Fleischer heirs, with one eye on “Barbie,” would like to exploit their biggest star before she goes bust. Fair enough; who wouldn’t? But a merch grab — in the lobby a plushie Pudgy goes for $35 — is not the same as a musical. The answer to “why?” should not come from mere marketeers.

Boop! The Musical
At the Broadhurst Theater, Manhattan; boopthemusical.com. Running time: 2 hours 30 minutes.