Ricky Martin has jaunty hair, shockingly white teeth, flexible limbs, shakeable hips, and a voice as smooth as oiled leather. Remarkable though it may seem, he makes an undershirt and suspenders seem a credible fashion choice. And yet, as many who have seen the recent Broadway revival of Evita know, he's just a little bit dreadful onstage.

Yes, he hits every mark and every note, sneers when called to, smiles when needed, but he does it all with the air of a talented trained dog. In saying this, I do not mean to cast aspersions on Martin's intelligence – interviews and album sales confirm his savvy – or his looks, which seemed much admired by many people in the audience. But his Che offered no interiority, no immersion into character. He did exactly what was asked of him externally, but couldn't conjure any sense of inner life. Writing in the New York Times, Ben Brantley called his performance, "polite, vaguely charming and forgettable. You could add "tail-wagging," too.

This phenomenon is not uncommon when Grammy winners come to Broadway. They have the moves and the range, but most favour a straightforward, indicative performance style that has only a tangential relationship to stage acting. A quick YouTube perusal of some recent stints – by Nick Jonas, Ashlee Simpson, Melissa Etheridge, etc – shows that while none of the pop and rock singers are awful (not even Ashlee Simpson), none holds a spotlight to the Broadway regulars. Poise and a sturdy diaphragm? Sure. Nuance, intricate emotional life? Not so much.

And yet, that isn't to say that no pop star belongs on Broadway or in the West End. Sometimes it's a matter of finding the right role for a particular voice. Country crooner Reba McEntire's film and TV acting have rarely impressed, but critics were unstinting in their praise for her title turn in Annie Get Your Gun. The New York Times compared her favourably with Ethel Merman, writing that she gave an effortless performance, making it "look so easy that you wonder why we aren't all Broadway stars".

And sometimes, musicians are revealed as natural and persuasive actors, as in the case of Mos Def, the hip hop artist who replaced Don Cheadle in Suzan-Lori Parks's Topdog/Underdog, offering a performance as surprising and evocative as any of his album work. Had David Bowie taken on more major stage work after The Elephant Man, perhaps we'd place him in that same category. And it's a tremendous shame that Tom Waits has contented himself with composing for the theatre rather than starring in it.

Then again, there are singers that one finds so delicious, so charismatic that it shouldn't matter whether or not they can act. Should Nicky Minaj declare that she longed to do a musical version of The Balcony or Lou Reed announce his affinity for Beckett, I'm sure you'd see me camped out at the stage door. So – should pop singers leave the stage to its veterans or are there crooners you long to see in the proscenium?