People would just grief more because they couldn't play the position they wanted.

Then they would get reports and increase their punishment significantly and make their account unplayable (except for supporting obviously, which is the key here). They would have to abandon their main account and start smurfing, sure but they would still be toxic assholes on their smurfs and very quickly be thrown back into the same punishment of having to play support etc etc.

Your suggestion is cool but LPQ in itself is a waste. It is just a dota 2 hell that exist only as an act of sadism. My suggestion turns the pool of LPQ punished players into a resource while simultaneously encouraging their rehabilitation far more than the current system does.