I think that the difference is that Post Secondary education is directly paid for by the student. If the education is sub par, then students will not attend since there are lots of choices. In k-12 education the "state" pays for the education and the students have very little choices if the education is sub par. I think that the best way to change k-12 education is have the student pay for it directly (for those who can't afford it provide a voucher). Guess what would happen to those schools which are sub par? They would be empty (or they would change very quickly)!
What do you think?