All I ever hear from teachers is bitching about how hard their jobs are. The only people preserving mediocrity are the teachers themselves. They choose to work for the government. They demand higher pay while their output is pathetic and that is being overly generous. Tell me why the pay should be raised when the majority of the schools are complete sinkholes for money and are terrible excuses for an education. If a private school educated its students so poorly then parents would immediately withdraw their children and resort to educating them at home.
Your solution of reward people first then expect them to perform on their end is simply utter nonsense. Offering higher pay won't draw more "dedicated" teachers. It'll just draw more fuck ups and more tax money will be pissed away on good for nothing jerk offs. This is why schools are now going by merit pay. If you don't perform then you don't get paid and that is how it should be. Those who perform will be rewarded with better pay while those screw ups won't perform and will have to find a new career.
In your rush to discredit a government enterprise, you neglect basic economics. If you offer more money for a job, more and better people will want to do that job. It works in the NBA. The NBA wants only the best point guards in the world, so they offer the huge contracts to get them.(And, of course, so Latrell Sprewell can feed his family)
This concept applies to every other field, why would it not apply to teaching? It is true that in the short term, you do end up paying bad teachers more, but this is so you can fire them in the long term. My point is, you can complain all you want about bad teachers, but if you just fire them, it doesn't achieve anything because we don't have anyone better to take their place. You can say "we expect better from you" or "get better or we will fire you," but those threats don't work so well when you have no reasonable way to back them up. Some teachers are inexperienced and will get better, and some might lack skills but be motivated and get them. However, there are some bad teachers that have no drive to get better and aren't going to get better. You need to be able to fire these people, and have better teachers available to fill their spaces.
You can look at Teach for America and see what I mean about attracting better teachers. The program gets students from top schools to come spend a few years teaching, but it's seen as charity work, compared to the money these people can make. They only stay for a few years. The program has gotten some results that way, but how much better could they do with that kind of career teacher? More money would entice some of these people to stay.
Merit pay, in concept, is a good idea, but the issue is, merit pay systems haven't reliably implemented a good way to measure merit. Test scores encourage narrow teaching and teacher cheating. Peer review is better in my opinion, but is used much less, and people complain about politics.
My proposal is that you simply pay teachers more across the board, and in exchange, they give up the ridiculous tenure options you can get and can be fired like regular employees. In this case, the tenure options are of greater value to bad teachers, who know tenure is the only thing keeping them employed, while the downside of not having tenure is not a big deterrent to teachers who know that they have to skills and intelligence to perform well. So trading tenure for more money makes the job's value rise for teachers who are good, or at least think they can be good, and makes the value fall for teachers who know they are incompetent.
As your privatized system, I will comment in depth later, but I think it suffices to say that, just as things are now, the rich would get a good education and the poor would get a lousy education. Good schools would charge high prices, ensuring that only the well off can afford to go, and use the money to hire the best teachers. The poor would be stuck going to the cheap schools that don't have the money to compete for good teachers. Partial government aid, as you suggest, would not fix this. The rich schools would make the gap as large as they could get away with, likely too large for small subsidies to matter much.