See, this is exactly the sort of thing that makes alternate history so attractive to me, the absolute certainty that people apply to historical events, that posits they HAD to happen the way they did happen. I marvel at how little had to change in order for things to have unraveled entirely differently. A few inches either way, and JFK would still be with us (well, he’d be 105, so maybe not.) And the Beatles were actually close friends, with no material differences between them, just personality conflicts that could have easily been overcome, and certainly with enough time elapsing.
Wings’ London Town outsold the Clash and it wasn’t even their best stuff.
It’s probably worth pointing out that Peter Jackson’s Get Back documentary cast at least some doubt on the long-accepted narrative that the Beatles were fated and doomed to break up during those sessions. Sure, there were the fights and tensions we’d already known about, but there was also footage of the guys getting along and discussing future albums and projects. Also, I recently read an article about a recording made during the Abbey Road sessions on which Lennon can be heard talking about the group’s “next album.”
So, there was maybe a chance they’d stay together awhile longer if not for Lennon’s meeting with Allen Klein.
Link added:
The way Abbey Road was recorded (with all four rarely in the studio at the same time), wouldn’t any subsequent albums pretty much just be their early solo work repackaged as Beatles records?
In 1969, sick and tired of the internecene goings on, George Martin is able to somehow, inexplicably, fire all four of them, and replace them with the Fugs, to become The True Beatles.
But John immediately went back to the stage with the Plastic Ono Band, and George too played solo concerts after the break of the band.
The decision to stop touring in 1966 was made out of frustration about bad stage tech (they couldn’t hear themselves because they had no monitors and the crowd couldn’t hear them neither from those tiny amps among all the screaming) and being unable to reproduce their sound on stage at the time. Both those aspects would have been overcome in the early 70s because the tech had massively improved and people stopped the steady screaming at rock concerts, as tours by comparable acts showed.
Hence my imaginary album including at least three songs the Beatles themselves had demoed or doodled with.
I’d bet good money that if they were all alive, what they’d be doing now is…
…something different* than anyone would guess.
These were Creative People. There’s no telling what that type of troublemaker will do…
.
*Think of all the bands who changed their sounds, even reinvented themselves…
Who would’ve guessed that Fleetwood Mac would leave the blues behind?
And the BeeGees desert the emo-folkie scene to go disco?
Or that Depeche Mode and Ministry would be synonymous with moodiness and violence, after their early upbeat ‘new wave’ bounciness?
How 'bout the early Beastie Boys, those “amateur hardcore punks” that were a support act for the Dead Kennedys?
Same with Sugar Ray, the “tough, raucous punk band that, overnight, traded their testicles for fame.”
And, of course, Pantera…you know, that early-'80s glam metal pop band?
There are dozens of similar examples. If all those bands can morph/reinvent/grow, why not The Beatles?
(Hopefully without Linda and Yoko mic’ed on stage…)
The Beatles had had plenty of bad experiences touring, up to and including jelly beans (George hated when they threw them; they hurt), The “bigger than Jesus” brouhaha came home when there was the sound of a backfire when they played in the South and they thought it was a gun. And then there was the incident in the Philippines when they were nearly beaten up by an angry mob.
Well with Ministry…their first album was a joke basically. A middle finger to whoever made them do that sound right down to a fake English accent.
Their next album was closer to what they wanted to do
Ironically, I like their first album
I think Work For Love is one of the defining songs of the 80s alternative sound.
If they intended it as an FU, well, sorry guys. it’s a great song, and a pretty good album. But you do you and be happy making angry music no one likes. 
I feel like this hijack is my fault. I just gave examples to point out that bands reinvent themselves, and I’d expect the Beatles to change as well.
So, please don’t abandon the Alt-Beatles subject to tout which version of which band you prefer…
Though, if you don’t like Peter Green’s Fleetwood Mac, I feel sad for you. 
OK.
I like my alternate Beatles where John left to make crappy solo albums with Yoko, but the Beatles didn’t break up, but instead hired studio musician and excellent guitarist Glen Campbell to replace John, and made Billy Preston the official Fifth Beatle.
Despite Campbell’s avowed disdain of those long haired types, he took to the songs and helped create a Beatles resurgence. Dreams of the Everyday Housewife became the new connecting song between She’s Leaving Home and Eleanor Rigby, with Another Day maybe never being recorded.
I think John meets Yoko, game over, he wanted to do other things. They could have appeased him by releasing Cold Turkey, but it just would have been all of the same songs under “The Beatles” name instead of solo names, who cares historically really.
I guess adding a fourth member was somewhat more likely in what if because fewer moving parts. Glen Campbell didn’t write his own songs so they’d have to be okay with outside writers on the albums. Eagles certainly made it work with new people.
You’ve still got a problem that George doesn’t want to play live and not so great a relationship between Paul and George. Paul had the opening after Cold Turkey, could have given it a go. But of the four of them, he was the one least willing to share the stage in any real way. John had Yoko, George did the Wilburys, Ringo does the All Star thing where other players sing half the songs. Paul would throw a bone or two to the others in Wings. Did the duets with Steve Wonder and Michael Jackson. But on stage, he never did the supergroup thing. Maybe he really was that bossy.
There was a period about 20 years ago, just after John Entwistle died, when I could have envisioned Roger Daltrey and Pete Townshend teaming up with Paul and Ringo to form a British rock supergroup. Maybe have Zak Starkey tag along as a second drummer and let him have a drum battle with his dad in the middle of Helter Skelter.
“The Boo.”
“The Beatles and Who?”
“Who Are the Beatles?”
The Whotles
I like the alternate history where Johnny Horton hears a Whotle.