I don't think it's a good idea. Randomness is something I try to limit in mafia games. Player-created randomness is one thing, but the GM shouldn't make it too difficult to discern what is happening.
On a mechanical level, I agree - mostly because basic things you want your players to know what happened and stuff you explain in the rules/mechanics and such in the OP. But I do believe, game-dependent, that things could be left obscure at times to make things interesting - so long as it is done in a balanced manner... which is easier said than done.