Von Callay
Getting Grilled by Special Agent Nixon
There's actually a Stephen Baxter short story - "The Twelveth Album" which discusses an additional Beatles album that comes out in 1971. The big advantage in that specific case is that all the Beatles actually wrote songs so all Baxter needs to do is discuss how they would have played these songs - John sings Paul's "Maybe I'm Amazed" is the specific big change he gives.
The thing with "adding" for music and art in general is that you're effectively saying that something you've come up with is better than or at least on the same level as what the artist originally came up with. It's not just a question of being an "accomplished musician" - with a bit of work and time I could probably do a decent-ish cover of a lot of the Beatles output (and a few others), but writing something that is plausibly "what John Lennon would have written" is insane!
Yes, exactly. Making up what they might have otherwise done is just a task that really falls beyond the writer's ability, unless you're going to brush over it or show it without showing it, just telling us they keep making great music without digging into any of the details, and if you're going to do that why are we here?
Thinking back, though, to the point about AH by subtraction, I could swear that I did read a Beatles AH story, I dunno, ages ago? where they go on in some fashion, or maybe they never really caught fight on a world-wide scale, so the story is about their faded glory as a middle-aged band playing to a moderately-sized crowd of people who stamp and cheer for them, but head out once the concert is over because the babysitter has to be home by ten, that kind of situation, and so the music they play is what they made, but viewed through this lens of weariness and cynicism about it that changes how it's thought of. Maybe it was a different band, I hate that I can't remember.