Are the succession process or role of the Champion explained anywhere at all?

We do see champions combating the antagonist Teams in gens 2-5, so are they peacekeepers? Was this them just taking responsibility as the strongest, or was this part of the title?

How come they remain the final boss after being defeated? Obviously you become the Champion in the end, so why are you still just some trainer able to challenge them all over again like nothing ever happened? Do they have to be appointed? Are they selected? Is there more to it than just being the strongest?