For the record, "Sgt. Pepper's" places third on my list of favorite Beatles albums, after "Rubber Soul" and "Abbey Road". And to be completely candid, I didn't like the album the first two times I listened to it (back in 1967).
All that aside, in some ways it might be the Beatles' most important album. It's true that it didn't live up to the original concept of the album, that of being music created by a fictional band. Only the first two tracks and the reprise support that concept. But then, there was the secondary concept: the idea that under the guise of being a fictional band, the Beatles were free to write and record songs that didn't fit into the Beatles' usual niche. They were free to write in any style or genre of their choosing.
Lennon complained that the album was just another Beatles' album and that any track from Pepper's could easily have been included on "Revolver". I don't see it.
Others have criticized the album over the years. Maurice Gibb, of the Bee Gees, said (at the time the Sgt. Pepper movie was being filmed) that he thought the album was passe'. Even Sean Lennon has panned the album.
In the years immediately after its release, other bands borrowed from the overall sound of Pepper's, which turned out to be the wrong move for them. Examples: "The Rascals", "The Buckinghams", and "Tommy James and the Shondells". The Rascals and the Buckinghams pretty much folded up like a cardboard suitcase soon thereafter. Tommy James squeezed out a few more hits, then did a Houdini from the music business.
Why? Because they wanted to SOUND like Pepper's without investing the time into writing in their own chosen styles. That's not to say that I didn't like those bands. I thought the Rascals' "Once Upon A Dream" had some merit. But these bands went for style over substance. Epic fail.
Bob Dylan has often been hailed as the most influential songwriter of the 60's, and there is some truth to that. But his influence on the Beatles, mostly John, was just that: Influence. John didn't try to sound like Dylan. He freed his mind to add more imagery to his lyrics, yet maintain his own personality in the process.
The bands who truly learned from "Sgt. Pepper" were the ones who began to think outside the box, not reproduce the box.