Tournament ranks should be awarded based on number of total entries paid, not the total number of players who entered. If people do enter multiple times then that would pull everyone up from above and help 'redistribute' some of the coin + ticket wealth.
I like having thousands of tickets and millions of coins, because at this point, accumulating those is just another objective in a game that lacks more - it's more of a motivation than a meaningless season rank that gets deleted from the leaderboard after a few months.
But I will, occasionally, take multiple shots at something like an arcade or pro 6-hole tournament. Not because I can't 'win' against the rest of the entrants, but because there's a tournament-within-a-tournament amongst the top few players and it's fun trying to hole out and shoot those absurd scores.
I don't like the idea of limited entries because it means tournaments can't be coopted for different kinds of play like that. But the game does need something a little different. Changing the rewards based on entries (not entrants) could work.
Another would be to have multiple-round tournaments (maybe as an extra version of the Weekly Tour?) where individual scores remain in the leaderboard and cannot be replaced with a single higher attempt.