I'd have no problem with a mastery point requirement. You know, get every champion to level 1 to be usable in ranked.
The problem is that it would be quite annoying to get 20 some champions to level 1, especially champions you want to play since they all have various BE costs. This will make ranked a lot more inaccessible for new accounts/players.
But for people like me it's just a nuisance. I'm a one trick pony, why do I need to level up a bunch of other champion mastery? Granted, I know how to play around 20-30 champions extremely well, but that's not my point.
Anyway, if you choose to only use champions that you've mastered in ranked then you have to figure that statistically your enemy team is more likely to use new champions than your own. On average you should be more experienced on your champion than your opponents. So over a decent sample size of games you should climb.
When I made an account this season I was one tricking Morgana support/mid as I always do. This was before she was updated, so she was pretty weak. Anyway, at first I was very worried about bronze because of all the hard inting people and just generally bad teammates and I'm playing a champion that isn't a hard carry.
Well it doesn't matter because the opponents in bronze are so atrocious they can't dodge a single Morgana binding. I just rolled over kids like they were bots. This continued until about gold 2. Then I slowly ground my way up to plat 2 where I've been stuck at since the Morgana bans took off 2 months ago.
Anyway, if people in Bronze want to do stupid shit then let them. You can definitely carry out of Bronze.