Although I wish this could happen, It would not be able to work for 2 Reasons:
1: A player must have at least 16 available champions prior to entering any sort of draft pick game. Many people I know (Including myself) only have mastery over specific champions. I mainly play Katarina Mid and Lee Jungle, and because of this, about 70% of my mastery points go into the alone. Many people don't have even mastery level 3 on enough champions, which means with this system, they wouldn't even be able to play ranked.
2: You can't be 100% sure someone isn't good with a champion Just because they don't have mastery. For example, bjergson might not have a very high mastery over Ziggs, but he is still very good at Ziggs, and can bring him into the right matchup and still succeed.
I think the better option would to require people play AT LEAST 5 games on someone before entering ranked, so that way they at least have an idea of the champion and their kit.