While I agree with you about the advantages of private schools, I disagree that government is the problem. The problem is LIBERAL government who, for at least the last 20 years, has watered down content to nonexistant levels.
Consider the education system in India. Free to all, and expectations through the roof. Those who don't excel in school become blue collars. The Universities are government schools, and they have higher standards than any in the US.
The answer to US public education? Raise the stakes. If you don't have, say, a 3.0 in high school, you don't go to college. Period. You go to trade school, or work for your father-in-law at the auto parts store. All work in honorable, and everyone can't be white collar.
A college education used to mean something, and it was not for everyone. Now it just means that you (or someone on your behalf) wrote a series of checks, and you showed up for the finals.
Can you imagine the uproar from the liberals if a conservative proposed a 3.0 minimum for entrance to state universities? But that is what it will take.
My assertion is that education would be better if it were a competitive industry, irrespective of government involvement. Education can still be taxpayer funded.
There is no surely reason to think competition would be bad, is there?