There is more than the one flaw.
People have suggested that idea before, and the idea is as untenable now as it was then. The sole purpose of this idea is defeated by the same fundamental flaw that the Mastery System has: Mastery rank has nothing to do with how well you play. It simply doesn't and that alone makes the idea dead on arrival.
League already has far higher ranked restrictions than other games and this would raise it further. It would suddenly lock players who are already ranked-eligible out of ranked and it does even not restrict based on experience. It restricts everyone including long time players who have far more experience and were playing before the mastery system. It would lock out the players with small champion pools who would, according to the "mastery reasoning", know their champions they are playing better precisely because of that. Especially one-tricks, and would force them to take days frustratingly grinding games on 14-15 other champions that they have no interest and no intention of playing in ranked, just to play Ranked.
And most important of all: Mastery rank has nothing to do with how well you play. There's plenty of people with Mastery Level 5, who flash their little icon in games and then die and throw and die don't know the champion they are playing or even the game at all.
The idea doesn't solve the one problem it is supposed to fix and causes a half-dozen others.