Tournament Team Limitation Selection [banning?]

A lot of people have mentioned-correctly, I feel, but this has been discussed before-that the number of bans should be increased.

I propose an alternate idea which would only matter for tournaments and such: Team limitation. Your team selects a certain number of champs, and from that point on throughout the entire tournament, they are only allowed to draw from that pool for picks.

Not sure if it's a good idea, but I thought it might be interesting to see what happens instead of simply "increasing number of bans."