"King of the Hill"

I'm a little concerned that by the start of the tournament, a rather large number of players will register, and many will have to wait quite a long time for their turn, which will significantly reduce interest in the tournament for most. I can suggest a more interesting scheme: after a player becomes the King of the Hill, other players are given N days to challenge him. And then, from those who issue a challenge, an opponent is randomly selected. This system will increase interest in the tournament and give a greater chance of playing to those who want to play soon.