I think your system has a number of faults in assumptions.
1. Should the person who first calls a role be the one to get it?
2. Does the last pick always have to be the one to support if no one else wants to? What if they only play mid and completely suck at everything else?
3. Should 4 people get to decide what character you get to play?
4. Won't this force the meta? and everyone else playing outside the meta get kicked from groups?
2. No, I never said that either. Read 1. That's not even relevant.
3. That's not what's happening here. This isn't just straight vote to kick, you're reporting someone for specifically doing something. i.e. No communication, AFK, Picking a champ for a role that's already been picked and locked in.
4. No, there's no option to report for 'not playing the meta'. Does that mean people wont make stuff up just to kick people? Of course not. But there's no immediate punishment, you just have to re-queue. Big deal. Whether or not there is to be punishment enacted is decided by the tribunal at a later time. That's why this system is hard to abuse.