Sit down we need to have a talk...
Sgt Pepper, while Paul may have driven it, was the beginning of the end. In my mind the Beatles had already peaked with Rubber Soul and Revolver. Post Sgt Pepper there wasn't much left. The White Album was essentially a bunch of solo productions and not even a complete production. The talent of the group though ensured it would be an amazing album. Abbey Road was another great album but again not on the level of Rubber Soul, Revolver, or Sgt Pepper. Same can be said for Let It Be. You're right that Paul took the lead in the Beatles starting with Sgt Pepper, but in hindsight, that's actually what started the decline of the Beatles. Everyone wants to throw Yoko under the bus, and she was surely to blame partially, but you can't discredit the fact that Paul was having it out with every member of the band. His control caused every member to quit at one point or another.
And truthfully, history has shown that Paul was actually the third best song writer in the group. That's not to say that he was terrible, but John and George were amazing writers. The songs Lennon wrote with the Beatles and solo, shit on everything Paul did. I do laugh at what Lennon said about Paul's controlling creative influences in the later period with the Beatles.