I think the list of champions that the other team bans should have a randomized order.

It may not happen often, but it has the potential to be abused the way it is now. For example, the game I'm in now, the jungler wanted to play Nunu, but the enemy team banned Nunu. From the ban order, we knew that it was the player who picked LeBlanc who banned the champion, so the jungler immediately declared his intent to spend the game camping LeBlanc. This doesn't exactly seem fair to me?