It'd be neat if at the end of a Treasure Vault run, when you hit the elevator, it displayed how many crowns each player picked up, sorted from "most crowns" to "least crowns". It'd give you an excuse to be vaguely competitive about it, sort of a fun little mini-game that randomly pops up.

Crowns would still be evenly distributed to every player, and there'd be no reward for coming in first.