"King of the Hill"

If, let's say, after tomorrow or in a couple of days, we have a "King of the Hill" game, why not have everyone play 2 games in a single-elimination format (16 players)? And then, from the remaining 4, a random draw decides who will play against the "King"? Maybe there are 16 players, but only 10 are actually ready to play. Why not let anyone who wants to play for the top spot compete for the right to challenge? I think if there are many willing participants, they will come up with a reasonable solution to this problem so that real contenders don't have to wait...