If you really thought about the dynamics of this game (think about the roles of doctor and cop and how they're played in this game), and how outside discussion would impact it, I think you'd realize just how DRASTICALLY having the option to selectively and privately talk to other players changes the game. If you get to do that, it's not even the same game anymore, the dynamics change so much.

Yeah, I'm not gonna deny that it might be fun and interesting the other way, but at that point you're not even playing Mafia anymore. *shrugs*

This is what Mafia is.