Wizardry 7 had something similiar to that. Where the chests would be empty if you took too long getting to them. Then you had to track down the people who had the pieces of the map. Though the NPC's couldn't finish the game before you, it made the game more interesting.

If someone did something like that I think it would still be fun to play. It would help get away from the theme of "You are the CHOSEN ONE, only you can save the world."