Champ select bans should be both Reactive and Proactive.
Currently they are only proactive.
By this I mean that each team bans 3 things they think are OP or do not want to deal with. THis is proactive.
More proactive bans are really not needed and making teams ban 4 or 5 champs proactively is not going to do anything but just have a higher pool of perma banned/take turns being banned champs. This is not really a improvement on the game overall.
However there is another kind of ban, Reactive.
Reactive is more strategic especially for non LCS games where you have no idea who you are going up against. The idea is to ban based more on what the enemy team seems to be planning based on champs they already have picked.
Examples? The enemy team has Ali and Malphite picked so you ban Orianna to prevent the cowball/rockball delivery from being a potential threat. Enemy team has Shen picked? Ban Twisted fate to stop the global ult madness. Enemy team has Yasuo picked? Ban Janna and Malphite so he has fewer means to use his ult.
How it would the pick ban order go? Both teams ban 3 champs proactively Then Blue team picks 1 and Red picks 2. Both team ban one more champ. Both team pick 1 champ to use. Both team ban one more champ. Both team pick 1 champ to use. Both team ban one more champ. Finally Blue team picks 2 and Red picks one.
Assuming 6 total bans on each side this would increase the number of champs involved in pick/bans to be 22 up from the current 16. And each player gets 1 ban except for the first pick who the first and last ban.