Honestly... I don't know about this.
I understand you're premise and agree that in general this would help league A LOT.
That said, consider a situation like the following:
There are 5 roles in league: top, mid, jungle, adc, support
I main my favourite role and have practiced 5+ champions in that role with no problems.
I have two secondary roles and have practiced 3+ champions in each of those roles.
I have two roles where I have only practiced 2 champions in, as I almost never play these roles anyways.
So I queue for ranked play with a very reasonable set up. I can play 3 roles really well, and if I get stuck in one of the two remaining roles I have two fairly confident picks in them anyways.
Then bans go through, and one of my two champions in one of the off roles gets banned.
Picks go through, I'm last pick, and the other 4 picks on my team took the 4 other roles.
My role-opponent took my remaining pick for that role.
So what do I do? I might own other champions in that role, I may even have tried them once or twice, or read a guide or watched a video on them, but I'm not allowed to play them because I don't have 'proficiency' in them.
I can't take either of my comfort picks because they're picked/banned.
So now I'm forced to dodge or 'troll' by picking a champion for a different role.
You could argue that I should practice more champions for those roles, but I think 2 champions in two off-roles is honestly quite reasonable and even if I got to 3+ it's possible that additional bans or multi-role champions could still exhaust the champion pool.
It may never be a problem for season 1 and 2 veterans, but for relatively newer players the required champion pool to safely play ranked would be overwhelming. I'd personally be quite turned off of rank. I don't want to have to go practice Top, a role that I don't like and that is sufficiently popular that I rarely ever have to play it, on champions other than the 2 I have chosen to practice for it, in the off-chance something like this will happen.