Sylvain, on your first point, I think we are saying the same thing. Education has both a private good element and an externality, which is why it should not be left to the market. The economic solution to such goods is for the state to subsidize the good, but leave provision to the market. I was suggesting that these markets should be regulated because they could be distorted (even if the private good element of education is high).
But education is not a public good in the sense of its being non-rival and non-excludable. The practice of the state's providing goods free of charge applies only to these pure public goods. That is why I was questioning why governments intervene in education as if it were a public good, whereas they should intervene as if it were a private good with externalities.
On your second point about principle-based arguments that support free, mandatory education, I would support them if they actually delivered quality education especially to poor people. The problem is that the current system is not delivering to poor people. And the reason may be that we are delivering as if it were a public good something that is really a private good with externalities.