The problem is that with more bans is that it doesn't fix any problems. When you look at the data, some champions are banned even though they aren't pivotal to winning or losing a game. They are merely perceived as being a pain in the butt and no one wants to deal with them.
Why do I ban Blitz? It's not because he's strong, it's because his pull is so annoying that when I support I don't want to play against it. If I didn't ban him, would their team automatically win? No, not at all, I could counter with morgana or just not get pulled. But I don't want to deal with it.
On the flip side, there are champions that are more powerful than others, and they are usually either picked or banned in any game. If we allowed the possibility for more of these champs to get banned, would that fix the problem? Probably not, since the next-most-OP champ would become the new standard, and nothing has really changed.