It has very little to do with the the overall total number of champions. It's that with 10 total bans you could pretty much remove an entire role from the game (ADC, and Support)...
Who
The
Hell
Cares??
With how stale the game is right now I would be completely fine with pro teams having to run some bruiser/mage, and support bot lane. Would definitely make the game worth watching again. The whole ADC and support bot lane has been set in stone (with the meta) and there is no way to change that unless something like this is implemented before they make more champions for those roles.
Really wouldn't be that big of an issue for solo queue other than people who main one role would be screwed over lol. Then again you would have to rely on the enemy to ban the same.