There's maybe one reason to allow players to ban picks from their teammates but it's not that significant and it gets outweighed by the reasons not to allow it.
Reason to allow it:
A last pick player may want to pick a op champion but there is a bigger chance for the enemy to pick it in that time so you ban the op champion so the enemy won't pick it.
Reasons not to allow it:
It's another way for trolls to sabotage games
If someone bans someone else's champion even for the good reasons there is a high chance that the game will result in either a dodge or a troll because of the player who's champion got banned. Personally, I get mad when someone bans my champion but I don't troll, I just dodge the match. And I think this is what most people do.
I'm speaking this from experience, there wasn't a single match where people were nice to each other when someone banned their champion. That's why I think this option should be disabled. Nothing positive happens when someone bans someone else's champion. Disabling this option will result in less dodged matches and less trolls and flame.