In this post here, Michael J Green linked to a CATO paper called Private Education is Good for the Poor: A Study of Private Schools Serving the Poor in Low-Income Countries. It’s not about America, but I remember that it had some very interesting information in it. Here is a link to a CATO Policy Report that has another article about private education in poor countries (this one is broken up, which is annoying).
Actually, I think it’s very possible that people will realize the government is terrible at teaching children. There was an article I read (which I cannot find, so if anybody might have read it I would love if you could post a link - I think I read it through these forums), which was about public schools in West Africa - I think Ghana specifically - putting private schools out of business. After some time though, the poor families realized that the public schools were junk and started going back to the private schools, even though they would have to pay.
If the poorest families in Africa can decide it’s worth it to pay for private schooling despite free public schooling, then I think it is entirely possible for Americans to realize this too. It just has to be worth it to American families. For something similar in America, there will probably have to be more decline in the American public school system, but considering the downward trend, I have no doubt this will happen.