5+ Bans per team would be good and here is why
TLDR: Too many champions are insanely overpowered (OP) in each lane + jungle and with there being 3 bans a team (6 total obviously) it makes it impossible to not have to pick OP champions to win. Having more bans when balancing clearly isn't doing a good enough job would be great.
The longer version: I feel like having MORE then 3 bans per team (6 total) would be greatly beneficial to the game at least currently. Just to give an example (although a bit irrelevant to the time of making this post) it was extremely common that Dr. Mundo, Tahm Kench, Rengar, Soraka, Brand, and Jax, were all banned. Most of the ranked games I was in had at least 4 or 5 of these bans. Now it seems to be Tahm Kench, Rengar, Udyr, Jax, Xin Zhao, and something such as Soraka still.
Now although the 3 bans per team, 6 total bans, while that covers a lot of important ban picks, the issue here is now things such as Fiora or Gangplank top, Fizz mid, Nidalee or Gragas jungle, Kog'Maw ADC, with a multiple amount of supports to pick from for bans. They all are free to pick from...
One of my friends brought up a good point I feel which is the champion pool is only getting bigger, and that's not counting the occasional champion disable from bugs. This point is completely true and I feel valid, and I am sure we can all agree on a lot of times when new champions are released, they are way too overpowered to let into the game at the risk of the enemy team having them so they are necessary bans, or they are way to weak but everyone wants to play them so you have to ban them or face the punishment for it.
As a final bit of recapping and more then likely new information that I am just adding in as I go: I feel like a MINIMUM of 10 bans is starting to become, if not already, necessary. There are to many changes that happen that are either to drastic or just flat out unnecessary (Such as the Dr. Mundo changes that made him be a practically necessary ban or you would get destroyed) and with changes to items or champions being VERY common, all it takes is one person to get out the news of a new champion being ridiculous and you got yourself a new necessary ban assuming that it's not an easy to counter pick.
One last bit to recap just to hopefully drive the point home: 6 bans that are currently common: Tahm Kench, Rengar, Udyr, Jax, Xin Zhao, Kog'Maw but there are tons of other high priority bans unable to fit such as Nidalee, Fizz, Fiora, Gangplank, etc. And with the new duskblade some AD assassins such as Zed and Talon are becoming more and more important to pick or ban.
Overall I feel like a minimum of 10 bans with how balancing seems to work with League, it seems like it should be in the game already but it isn't so I feel like it is practically necessary to have, even if not 10 bans all year around at least during LCS or worlds.