Regeneration is, as far as I'm aware, just something they retconned in after the first Doctor decided to quit and they didn't want to end the show. I imagine if reddit/redcafe were around at the time people would have been up in arms about the silliness of the whole idea, but here we are now discussing it as if it's perfectly fine.
The point is that as much of fans of these shows like to obsess over cannon they're all fundamentally trying to get around that simple problem. That real people who age, change, and have other motivations and commitments are depicting fictional, timeless characters.
Sean Connery and George Lazenby are pretty similar looking dudes, but George Lazenby wouldn't win a Sean Connery look-a-like competition, but it's not real life and audiences learnt to just roll with it, would any of the Lara Croft characters be mistaken for one another, or do any fans on Game of Thrones really care about characters being recast between seasons?
None of it really matters, it would take a minuscule amount of universe building to justify any change and fundamentally we watch (or don't watch) TV shows based on whether they're good or not.