Ringo, being a cardboard cut out marionette manipulated by George (his friend Terry Gilliam helped him with it, the big issue being sometimes Ringo was a giant hedgehog) was in no position to refuse Yoko's request.
If Lennon had not met Yoko, Linda would have sung in The Beatles with Lou Reed wearing his McCartney mask, Paul being dead, and that would have done for The Beatles. Linda being Lori Anderson in a mask, of course. Carole King kept writing most of the music as Reed couldn't manage the jaunty, twee output contractually required, but it did keep him going after Velvet Underground split up (that was Yoko too).
I think it's been James MacAvoy playing McCartney for the last decade, which is why Paul McCartney was not in The Last King of Scotland, etc.
One point I failed to mention is that initially Lennon tried to replace McCartney with a walrus, which went very badly due to insufficient fish backstage, hence Paul being a cardboard cut out later on. Despite 'Paul' eating 17 large haddock in a row, still George failed to notice as the walrus was actually pretty good on bass and the vocals were spot on.