So their manager had a drinking problem and a drug problem and he died less than a year after Paul "allegedly died in a car accident." And Paul's girlfriend broke up him after the "alleged fatal car crash where the real Paul allegedly died," and her father died the same year as the manager. Is that correct? Some untimely deaths there. Could make people wonder. I looked up Wikipedia on the guy named "Billy Shears" who was mentioned as a new band member in their album St. Pepper and Wikipedia writes it was a person who never existed? Interesting because the link I read today showed pictures of this man named "Billy Shears" and he certainly looks a lot like Paul. Of course if he took someone else's identity it would bode well to pretend he never existed. I also noticed a bad attempt to photoshop his picture, note the chin in photo post #11. Why go to such trouble to photoshop a picture if there is nothing to hide? Odd. I also read that Paul came out a few years ago stating it was a hoax created by the Band. Funny he felt it so important as to explain it all these years later after the other band members are dead (short of Ringo). I'm wondering with the fame they were enjoying does it make sense that they would create such a hoax? What could possibly be the motive for making up such a story? They were already famous. On the other hand, what would be the motive for covering up a band member's death and finding "another Paul?" The future of the band was at stake. That would certainly be a motive. Always look for motive guys. That is key in finding the truth.
No Beatle ever claimed it was a "hoax created by the band" The Beatles had ceased to exist as a band by the time it came up (their last recording as a quartet was completed in Summer of 1969, specifically the song "Because"). The whole theory was dreamed up as described in the OP and then supplemented by people looking for "clues" and reading in what they wanted to read in (for example PM walking barefoot across Abbey Road).
Actually there was no car accident; it was a moped spill, not serious but enough to cut McCartney's lip, that supposedly spurred him to grow a mustache to hide the scar. That accident happened while riding with Tara Browne, an Irish friend who was an heir to the Guinness fortune. Tara Browne later would be killed in a traffic accident in his Lotus Ëlan when he sped through a traffic light and crashed. That is what Lennon was writing about here:
He blew his mind out in a car
He didn't notice that the lights had changed
A crowd of people stood and stared
They'd seen his face before
Nobody was really sure if he was from the House of Lords
He didn't notice that the lights had changed
A crowd of people stood and stared
They'd seen his face before
Nobody was really sure if he was from the House of Lords
(Browne's father was in the House of Lords for 75 years)
--- but that moped accident was used as a pretext for LaBour's fantasy story. The 'motive' was simply an amateur writer trying to find an original angle, and it got out of hand.
As is often the case, the simple explanation is the correct one; no need to read imaginary sequels into it.