Why are players allowed to ban champions?
Banning means we don't always play our mains. It might also make it harder to play champions that are interesting or unique, but initially frustrating. The champion could be balanced but, when it's new, hard to play against. So interesting and unique champions wouldn't be played so much. Then they'd get nerfed too far and they get played a lot less again. Riot works very hard to create unique characters, sometimes this could mean they will be played less.
Banning may also discourage players from the habit of thinking outside the box and creating strategies against troublesome champions.
Why ban at all? I don't think it is a good idea.
.
rework is the biggest mistake riot ever made