I like this idea, as it is a common system on many online games.
Regarding banning cheaters, I agree that sometimes innocent people are unfairly accused, and occasionally, an alternate user on one machine can get banned, and that would affect another innocent player who uses the same machine.
Maybe it would be more efficient if admins first temp-banned an alleged cheater (for a week, or however long admin feels is necessary), and then perma-ban on the second offense.