@Tettleton Chew
Let me start of by saying, I have experience (though in small quantities) in teaching. I've gone through a public education. What I am about to assert has both reason and experience to support it. That being said, here goes.
1) Parents truly have no way to identify a truly good teacher from a truly bad teacher. Simply said, parents have minimal direct interaction with teachers and therefore are unable to accurately judge the teacher. Their only source of information comes from their children. The child, if intelligent enough, could possibly tell the difference. However, even the opinion of the child is unreliable as the child is directly affected by and interacted with the teacher, and therefore a personal bias is introduced.
2) I believe the "law of diminishing returns" applies here. A good teacher, even if identified, has a limited class capacity. Apologies, but even the simplest of children surely realize this. A good teacher given a class of 1000 will simply not be as effective. In essence what I'm saying is: the good teachers can only teach so many students. There aren't enough good teachers for everyone.
3) Giving the parents the choice of school simply isn't ideal either. What you fail to see is that a class with above average and under average students mixed together is no different for the under average students, and almost detrimental to the above average student (with potential accounted for). In general, private schools are better than public schools. This is because of both students and teachers. The students at private schools are GENERALLY of higher caliber than those at public schools. (that being said, remember I am also partially a result of public education). This general separation is beneficial for both high and low caliber students. The lower do not feel the pressure to compete with the higher, and the higher are not limited by the lower.
Your "plan text" (in the words of a policy debator) is simply unreasonable and impractical. Even if it could happen, it would simply be for the worst. The system, as bad as it is, should not change the way you propose.
All that being said, I'm only nineteen (still a university sophomore). Feel free to use that against me (though if you do, keep in mind what may be inferred if that's the best argument you have against me).