If they required you to have a certain mastery level, they'd also have to make you do it on a minimum of 16 champions, and that's bullshit. I have one champion at level 5 (Nami), and until recently didn't even have anything else at 4 (but now Blitz and Soraka). Other than those, I have only 1 at level 3 (Gangplank).
So basically, even with your minimum standard of Mastery 3, I am only 1/3rd of the way through being able to even enter ranked play, yet I've climbed more than an entire tier from last season across almost 150 games. Why would Riot kick me out?
Your system targets a certain type of person, yet punishes everyone by default for no gain. Mastery level doesn't even equate to proficiency.