“I knew instantly you can never play Beatles songs on screen because the copyright is too expensive. So I’m thinking, ‘How would you do a Beatles episode without Beatles music?’ And that becomes the entire plot,” Davies explains. “That’s where the idea came from – copyright law!”
IIRC I think in some bit of extended lore it says that the Doctor can’t go to any more Beatles gigs because there’s already some version of themselves at every single one so it would be a time paradox lol.
Also in 2020 someone made an entire David Bowie biopic without having the rights to any Bowie music at all!