A moment I barely noticed in the 2019 Broadway production of David Byrne’s “American Utopia” jumped out at me with new resonance in Spike Lee’s film of the show for HBO.

That was when Byrne, in his introduction to the song “Everybody’s Coming to My House,” described hearing it performed by students at the Detroit School of Arts. Without altering a word or note, the high schoolers had turned the number, which in Byrne’s original version comes off as an anxious monologue about being inundated by otherness, into a joyful choral invitation.

“I kind of liked their version better,” Byrne says, apparently amazed by the material’s mutability: The song was the same yet had “a completely different meaning.”

I knew what he meant; after all, I was watching an even more elaborate translation, in which a concert staged like a Broadway musical was turned into a live-capture television film for cable. And though Lee’s slick and exuberant adaptation includes plenty of shots of the audience at the Hudson Theater bopping to the beat and dancing in the aisles, it was now, like “Everybody’s Coming to My House,” the same yet totally different.

Theater lovers are getting familiar with that feeling. These days, it seems like everybody’s coming to our house — and walking off with the furniture. Not for decades have we seen so many Broadway shows, whether musicals (“Hamilton,” “The Prom”) or plays (“What the Constitution Means to Me,” “The Boys in the Band,” “Outside Mullingar,” “Ma Rainey’s Black Bottom”) or unclassifiable offerings like “American Utopia,” taken up by Hollywood, squeezed through the camera lens and turned into film.

The squeeze is certainly subtler now than it used to be. Lyrics are seldom butchered to avoid offense as they once were; I expect that Steven Spielberg’s version of “West Side Story,” scheduled for release in Dec. 2021, will restore Stephen Sondheim’s original rhyme for “buck,” which had to be altered for the 1961 film.

Nor are innumerable songs dumped like dead plants from fire escapes anymore. (The 1966 movie version of “A Funny Thing Happened on the Way to the Forum” dropped at least half of Sondheim’s 14 numbers.) Musicals — and, in a way, plays too — are now being filmed because of their music, not in spite of it.

Of course, you expect that hands-off treatment from the Disney Plus live capture of “Hamilton,” which in its content, if not effect, was a near replica of the celebrated stage version. But even “The Prom,” though not a blockbuster on Broadway, emerged from Ryan Murphy’s Netflix translation with all its songs and then some.

That doesn’t mean these works are unchanged. Compared to the stage version, Lee’s “American Utopia” feels grander, more elevated — sometimes literally, with its shots from above.

“Hamilton,” on the other hand, with its frequent close-ups, especially of the women characters, is a much more human-scale story onscreen than it seemed to be on Broadway. Swirling hand-held cameras suggest the intimate chaos of lived experience in a way no choreography framed for a proscenium could. Whether that is an improvement may depend on whether you prefer your history personal or formal; I like both and refuse to choose.

The movie of “The Prom” definitely went for the personal — in part because of Murphy’s biographical connection to the book of the stage musical, by Bob Martin and Chad Beguelin. Like the character of Emma, Murphy grew up in Indiana, had an unhappy coming-out and could not take the date he wanted to his prom.

The stage show seemed to alternate between telling that story and satirizing four narcissistic Broadway performers who, in need of good publicity, decide to help Emma whether she likes it or not. In the movie, though, three of those four interlopers feel like supporting characters, despite being played by Meryl Streep, Nicole Kidman and Andrew Rannells.

The fourth, played by James Corden, is given so much more emotional heft — not to mention an onscreen mother referred to only briefly onstage — that the movie is as much about the healing of his own gay scars as it is about Emma’s getting to dance with her girlfriend.

I understand, and was even moved by that choice, but it takes a lot of the fizz out of the material, replacing it with syrup. And the cast, starry though it is, cannot compensate. I kept hoping that the superior original Broadway performers — journeymen including Beth Leavel, Brooks Ashmanskas, Christopher Sieber and Angie Schworer — would descend on the film the way the Broadway characters in the story descend on Indiana, to show the rubes how it’s done.

Recasting a play with stars for the screen used to be the rule; I need only say the words “Lucille Ball is Mame” to set musical theater fans’ teeth rattling. The excuse is always money: It takes big names to sell enough tickets to offset the enormous budgets of film. I’m not sure whether Emily Blunt and Jamie Dornan are those kinds of names, but their appearance in the screen adaptation of “Outside Mullingar,” called “Wild Mountain Thyme,” is the least of that movie’s problems.

The most is John Patrick Shanley, who wrote both versions and, catastrophically, directed the movie. (His direction of the film version of his play “Doubt” was better, but so was the raw material.) Exaggerating everything bad in “Outside Mullingar” — its bizarre plot twist, its encyclopedia of Irish clichés — he smothers the small spark of what was good in it: the tale of a man so locked in by shame that love can find almost no way to enter.

Following what used to be stage-to-screen protocol, Shanley has also made the mistake of “opening up” a story that was better off shut down. Placing Blunt and Dornan within touristy shots of the Irish countryside does no more to make the material filmic than the addition of an unnecessary character played by Jon Hamm, paired off with an even more unnecessary one, makes it richer. This is a case of the moviemaker not respecting the playmaker’s material, which is especially odd given that Shanley is both.

The best adaptations today do not feel like rescue missions or charity makeovers; they relish the theatricality of their sources and try to enhance, not disguise it. Joe Mantello’s powerful Netflix rendition of “The Boys in the Band,” based on the 2018 Broadway production, does make a few poetic forays into back story, but mostly, like the play, stays put in one place on one evening. The compression makes the whole thing tick like a time bomb.

That’s also how I felt about Viola Davis’s huge and hugely pressurized performance as the blues singer Ma Rainey in the otherwise patchy Netflix adaptation of “Ma Rainey’s Black Bottom.” Her expressionistic makeup is demure compared to her emotional makeup: She is a woman who knows that her voice is the only capital she has in a world run by racism.

Whenever the director George C. Wolfe and the screenwriter Ruben Santiago-Hudson stick close to August Wilson’s original story and its claustrophobic setting — a Chicago studio in which Ma is about to record with her band — the movie maintains the play’s long-fuse tension. But that power dissipates the moment it steps outside for context, as if context were necessary in a plot whose themes of appropriation and resistance are as relevant now as they were in 1982, when the play was written — or for that matter in 1927, when it’s set.

The best scenes in the movie — like the one in which Ma insists that her nephew be allowed to deliver a song’s introduction even though he stutters — use the camera as a highlighter, emphasizing the structure of the argument. These moments do not try to simplify or, worse, overplay that argument, instead trusting that film, contrary to its reputation as theater’s flashier but less intellectual sibling, is capable of delivering complex verbal ideas like Wilson’s.

But is it a film? Most of these recent adaptations were made for streaming services, with economics and aesthetics completely different from those of the studios that made the classic ones. People who saw the 1972 movie of “Cabaret,” to name an almost universally admired film transfer of a musical, saw it on a screen even larger than the proscenium at the Broadhurst Theater, where it originally ran on Broadway. But most people who see “The Prom” today will see it on devices that fit in their den or their palm. No wonder its story got pumped up.

The best of the recent adaptations do something subtler. Instead of enlarging the action, they bring it closer, pulling us right up to the edge of the caldron and then tossing us in.

For me, this was especially true of “What the Constitution Means to Me,” Heidi Schreck’s play about lives lost in the shadows of our foundational legal document. Marielle Heller’s gripping live capture for Amazon doesn’t change the subject at all but, in a way, reverses the angle. We’re asked to situate ourselves in Schreck’s consciousness instead of our own — just as Viola Davis demands that we understand what it is to be Ma Rainey and as Spike Lee, in “American Utopia,” forces us to see the world through David Byrne’s antsy eyes.

In the theater, we are our own cameras and editors. We see what we choose, frame it as we like, and relish the right to maintain the long shot. The paradox of the best film adaptations is that we love them for doing the opposite: They put us onstage with the story and give us no say.