I also think this is a good idea.
However, how do we stop people from cheating? Perhaps a rule which states if you time out and the AI takes over, you forfeit? I know it sounds harsh for those with bad connections, but in the end, it's only a game. Perhaps we should have someone watch over the games?
An unofficial tournament is pretty easy to do. All we'd have to do would be to make a sign-up page and have people post their in game names and timezones, then match people by compatible time zones at first and in the end, try and arrange a good time for both players.