Bragging rights.

Seriously though, the rare treasure and unexplored lands are not usable in the game (some would be seriously cool!). Mainly they are references to previous FF installments. You do get gold stars next to your Treasure and Unexplored Lands menus for getting everything.

If you want to get every proposition reward, check out the frontsite for the list that I developed with Despotus. Unlike the ones in the game manual, this list is 100% accurate.