An Idea for Bans

Riot often espouse the rhetoric that League of Legends is a 'team' game. One thing that has often bothered me about - what one may call - trope, is that of the bans. If League of Legends is a 'team' game, why give the power of bans to just one person?

It's annoying, sometimes, when someone bans only the champs he can't fight, or troll bans, or whatever. I think that a good way to remedy this would be giving the first three players in champion select one ban each. That way, even if those three players only ban the champs they can't play against, it'll be a more balanced set of bans than just allowing one person to have at it with the chip on his shoulder.