Generally speaking, that isn't what bans are for. Bans should more or less, help you increase your odds of winning.
Yes, certain Supports can be annoying, but unless those supports significantly increase your odds of defeat. (particularly if it would counter the comp you want to run.) then it's not really worth a ban.
Personally, the fact that supports draw very few bans, suggests that supports as a whole, arn't impactful enough in games. Though champs like Alistar, Janna, and Braum, are notable exceptions, and have drawn bans in the LCS.