Why does it matter? Once we're in a game with them there's nothing we can do about it other than report them. That then goes to the admins and they can see this information.
And If you take exploiters in to account of the game, then it makes sense to change the no cool down, so I guess I change my idea about that part
It would matter in allowing people to leave the game first turn so they gain no benefit when they do see who it is. We would have to change votes to tweak then I guess if you want cd now.