This was a really good answer but I also don't think it invalidates the GP's point. There was a particular set-up at a particular time that meant that pop music was going to go very big and that explains more of The Beatles phenomenal success than your very interesting points do. Your answer explains some of how The Beatles became more than the average pop group but they still ("She loves me, yeah, yeah, yeah") started off as just a (boy band) pop group.
It's She loves _you_, yeah, yeah. Little quirks like that (using second person) set the early Beatles records apart from contemporary boy bands and were a forebode of that they were more than just a boy band.
There was a particular set-up at a particular time that meant that pop music was going to go very big and that explains more of The Beatles phenomenal success than your very interesting points do.
Pop was already big, see Elvis. If The Beatles were not as exceptional as they were, they would have maybe two or three hits and disappear, like most bands of the time. They were exceptional songwriters, who stood relevant for almost a decade, because they infused new ideas (e.g. from avant garde) into pop music. In contrast to e.g. Frank Zappa, they were able to convey these ideas to a large audience.
Around 1969-1970 they started to loose their edge. After a wildly experimental period (~Revolver to Magical Mystery tour) they slowly returned to more conventional Rock & Roll (see e.g. the album Let It Be). If they hadn't broken up in 1970, they would've probably become less relevant after then. E.g. even though McCartney's songwriting was still good in the 70ies, the world had moved on (disco, punk, etc.), with the ex-Beatles becoming less and less relevant. Except perhaps Lennon, who would work with more contemporary artists like Bowie.
GP stated that the Beatles were inevitable, that somebody would have come along with catchy songs and "star power."
That part of the GP's post makes little sense to me. There were plenty of post-WWII (and pre-WWII) popular music stars who fit that description.
Yes, an endless parade of popular music stars was inevitable, but something like the Beatles wasn't. Pop would have evolved with or without them, of course, but their impact was insane.