Sylvan, thanks for those thoughtful comments. First, by a public good, I mean a good that is both non-rival and non-excludable. Education does not have these characteristics. Yet, societies behave as if education is a public good (under this definition) by financing and providing it for free to everybody. This is the appropriate policy for genuine public goods like national defense. Education, on the other hand, has a large private-good element (in the sense that the benefits accrue to the individual), although--as I suggested--there are externalities associated with education. The appropriate policy for such goods is for the government to subsidize education and allow the private sector to provide it. But the problem here is that the resulting education "markets" may have many distortions, in which case--like with other markets with distortions--governments should regulate them. In the current situation, these markets are cropping up organically (reinforcing the point about the private-good element in education) and, instead of regulating them, governments are either ignoring them or trying (unsuccessfully) to make the flawed "education-as-a-public-good" model work better. And the losers are the poor children, for whom education is critical to escaping poverty.
This brings me to your second point. While I agree that there may be more to education than getting children to learn, I hope you will agree that the latter is fundamental, and if we are failing at that, something needs to be done.