Director Danny Boyle’s “Yesterday” suggests a number of Beatles titles. “You Can’t Do That.” “Run for Your Life.” And, mostly, “Help!” Any movie that champions the Beatles is on the righteously right track. (“Anyone who is against the Beatles is against life,” a character in a now-forgotten film once muttered, memorably.) The story is based on such an audacious idea it should almost be granted immunity from prosecution. But how did such a crazy premise—a world in which the Beatles basically have never existed—turn into such a routine romantic comedy? To paraphrase John Lennon, Mr. Boyle should have known better.

Considering that Beatles music is the movie’s foundation and its principal marketing device, it’s hard to buy into the movie’s anti-exploitation message, never mind the narrative: Singer-songwriter Jack Malik (Himesh Patel) has finally given up his dream of stardom, or even local success in his English seaside town, when the entire globe experiences a 12-second blackout. And just at that moment, Jack is hit by a bus. Before he even leaves the hospital—a couple of teeth short of how he started the day—he gets the hint that something’s amiss. “Will you still feed me / When I’m 64?” he asks his doe-eyed manager and biggest fan, Ellie (Lily James). She gives him a confused look. He gives her one back.

After he plays the song “Yesterday” for some friends, who credit him with writing it, he Googles “The Beatles” and finds nothing. No “John, Paul, George and Ringo” either. Coca-Cola has also disappeared, for no explicable reason, as has the band Oasis, which may be the movie’s best and most inside-y joke. But the point is, Jack immediately realizes that the Beatles library is a gold mine, ripe for a rip-off. (The movie, wisely, avoids “Baby, You’re a Rich Man.”)Despite the larcenous premise, there’s a sweetness to “Yesterday,” and some terrific covers of Beatle songs by Mr. Patel. The singer-songwriter Ed Sheeran delivers a very generous performance as himself: Having heard Jack’s demo, he invites the unknown singer to be his opening act, first stop Moscow, where Jack plays a raucous “Back in the U.S.S.R.” to thunderous applause, realpolitik be damned. At the after-party, the bruised Mr. Sheeran suggests to Jack that they both leave the room for 10 minutes, and whoever comes back with the best song wins. Jack comes back with “The Long and Winding Road.” Mr. Sheeran is crushed. “You’re Mozart,” he says. “I’m Salieri.”

That’s the kind of smartness one expects, at least from the Danny Boyle of “Trainspotting” or “Millions,” but the screenplay here is by the Richard Curtis of “Four Weddings and a Funeral,” “Notting Hill” and “Bridget Jones’s Diary” (rather than, say, “Mr. Bean”). As such, it relies on a catalog of clichés that seem to stretch across the universe. The inevitable Jack-Ellie romantic collision is tortuously delayed; Jack’s inept comedy sidekick, Rocky (Joel Fry), is the kind of movie device that predates sound; the logic of the situation has to be dismissed outright, or viewers will spend all their time trying to figure it out. In all his vetting of the Beatles songbook, did Jack ever Google a McCartney family in Liverpool, or the Harrisons or the Starkeys? It’s not as if the people never existed, only the band, and the logical conclusion of all this speculation is exactly where the movie takes itself. I don’t want to spoil the party, but it feels like exploitation.

Mr. Patel is charming, personally and musically, and Ms. James, while not given a lot to do, is certainly the winning presence she’s been since “Downton Abbey.” Kate McKinnon, as the stereotypical Los Angeles music-industry bloodsucker/agent Debra Hammer, is given such an awful, cartoonish character to play that she seems to have resorted to doing a Jeff Goldblum impersonation (to a point where I wondered, doesn’t she always?).

For all the musical affection, a gnawing omission in “Yesterday” is the human side of the Beatles phenomenon. They were endlessly charming, they sang innovative harmonies, they used chords that Elvis never dreamed of. But in the scattershot use of great songs, “Yesterday” misses the point that “The Beatles” was also a body of work. It evolved. It took pop music on a journey. The late songs were elevated by the early songs, and vice versa; they made sense of each other. There was a continuum that fans did, and do, understand. To be against “Yesterday” isn’t to be against life. But the film does sidestep something essential about a band it otherwise venerates.