A very pertinent question came up in the most recent "Ask Riot" session which you can view here. The question was "Can you add more bans to champ select please?" The questions refers to the champion banning select screen after you select the character you'd like to play, which is by no means guaranteed as you and the opposing team get to choose their bans for that game of the champion they do not want to play against.
They developers responded that bans overall per game have an intrinsic value as we have an idea of who we are going to play in that position, what our style is going to be and what we don't want to play against, that's how we select the ban. But to add more bans, for example from 10 to 20 (two bans per person) there are positive and negatives. Positives are more control over bad matchups and a small strategy increase if you are playing in a team ranked game where you can build a really good team composition and know that most of your weaknesses cannot be countered. There is of course a trade off that the opposing team can always ban your picks as they would have two bans each too!
The negatives they have stated is increased complexity to the champion select phase, this can take quite long if people keep banning the champions you want to play and make players leave or "dodge" (let the timer run out) making the game restart and you have to queue up again. It also reduces the ability to play who you want, I know for one I will never get to play Morgana again if the bans increase to two per player because you'll ban your direct counter and then ban a highly played champion in that position, in my case Morgana support.
At GameFront we are of the opinion that keeping the ban to one ban per player is where the game needs to stay like what the developers have said. It produces the perfect balance of each person picking their direct counter and no more which seems fair. It also means that when you're thinking of your counter pick you get one choice so use it wisely, instead of you can pick one which is your direct counter pick and then the other you just want to harass the other team to not allow them to pick that champ. As I said above it would mean the champ select process becomes overly complicated and a mini-strategical battle before the game has even begun, which if you lose you are likely to dodge or leave the game resulting in an endless queuing cycle where it takes you an age to even get to play the game. Let's keep it where it's at and let Riot focus on improving what they need to and balancing the game further in other areas.