The idea of a closed setup is that you have specific mechanics that could conflict with each other. If the 3mafia game had been open, the gameplay would've have been so much lamer. Closing the setup allowed the weird setup to function as it should've - people needed to figure out how many mafia were there and combat them.

Well, that actually didn't happen - closed setups are a really asshole thing to do. There has to be a reason for every role in your game and why the game needs to be closed in order to work properly.