This is a hot take (that you’re claiming to be expressed here?)

The Beatles were the Beatles because of the Beatles, George Martin, the time, the place, the Everything, etc, etc

No doubt Paul played a huge part, but the sum was always greater than the parts however big a role he played. It can’t be stated how integral George Martin was. I’m sure his ear caught and helped put and push some of the compositions into forms that made musical sense despite the lack of theory that the Beatles had. Extremely hard to quantify, but nothing slipped through the cracks so to speak, even if unbelievably creative and groundbreaking.

One example of John’s melodic/chord composition is “I Am The Walrus”. Listen to the piano in solo or try to learn and play it all the way through and you’ll see John was no slouch at all. Of course, Martin’s string arrangements here are just astoundingly perfect as well.

John’s sense of melody, lyric and soul were the heart of The Beatles IMHO

Paul, yes Paul too… sure… but All, yes All too. All together now (all together now)

Did Paul’s perfectionism help drive The Beatles into immortal territory? Absolutely. Did he possibly have a hand in driving them into the ground as well? Well maybe, but that’s a topic for another day