In Pokémon, especially the games, the player defeats the current champ. After defeating him, the team is registered and the player start... at home. Then the player can roam the country and even defeat the old champ as often as he likes. And he still is in the same place, in the champ room.
So, is there a in-universe explanantion why the player is allowed to roam freely, while the old champ has to stay put?
According to the Pokémon wiki:
Once you defeat the Champion, you are recognized as the champion, although in the games the player declines the position and allows the previous Champion to reclaim their spot.
This is unsupported by references, but it is clearly possible, since in Pokémon Black and White, N refuses to take the position after having defeated Alder.
In light of this fact, the most sensible explanation for the player being able to go back and defeat the old champion that that they refused to take the job.
I would say this is because the quest of the game is not to defeat the league, but rather to complete the Pokédex.
Such quest can't be done if the player is stuck battling for the league after he's defeated it once.
So he'd go "Nope, keep the old champion, I've got other things to do. I'm 10 years old I'm not old enough to work full time for you anyway"
Both in-game, and in-anime, gym leaders are not absolutely required to sit and wait for challengers.
In most of the games, there is a fetch quest of some sort to get the gym leader to go back to their gym so you can challenge them.
In the anime, Brock and Misty are both gym leaders, who leave their gyms but retain their leadership for a time.
