To quote Cameron McEwan at BBC Worldwide on Twitter:
50 years ago today, Doctor Who fandom was truly launched with fans moaning, “The new guy isn’t as good as the one before!”
It’s the idea that let this show run for half a century, especially when Patrick Troughton didn’t just play a rejuvenated version of William Hartnell’s Doctor but the role changed to suit him.
It’s very obviously an idea brought into the fiction from practical concerns, but it has come to matter to the story, especially with other Time Lords changing as well - and usually being better at it than the Doctor, as they can stay similar across regenerations more easily in smaller roles. I’ve run with that in RPGs, where recasting isn’t necessary - Kai in The Door In Time is really good at regenerating under stress, for example.
And I’ve used regeneration as a plot hook a few times. Its power can ignite dying stars, save (and change) other lives, burn, and more, and it allows a skilled user to become someone else even if they don’t need to heal...