I do not think it is correct to only allow a team to ban champions the other team has available to them. By doing this, you give the team with the most champions an advantage beyond team composition. The other team should not be aware of what champions the other team can pick. If the team wants to ban Garen, they should ban Garen; if the other team doesn't have Garen, so be it.
By giving the other team this information, you provide them an advantage that I believe RIOT has tried to avoid throughout the making of this game. Once you are in game, what you have purchased through RP should not hold any impact towards the games outcome. It is clear that in ranked games, the champion selection IS part of the game. It is obvious that team composition and selection flexibility is impossible to fix with the games champion buying system, but the other team should not be handed the other team's champion pool by default.
Here's an example of where this advantage is apparent:
I'm playing 3's and I know Morde and Lee Sin are very big champions in this map. As the game starts, I notice that both Morde and Lee Sin are not even available for me to ban. I simply force the other team to waste both of their bans on Morde and Lee Sin, or I grab them myself. I should have to take a risk by choosing not to ban these champions, yet with the enemies champion pool given to me, that risk is completely taken away.
To fix: Simply show all champions in the banning phase.