You are arguing something completely different. I pointed out that before public schools, there were large networks of private schools. Public schooling started as a response to the success of catholic schools.

I am not arguing for superiority of one over the other.

I'm just pointing out that decentralized, distributed decision making led to people's educational needs being met before government got with the program.

Also, your articles are on public v generic private. Catholic schools are outliers in the private school space. They tend to be significantly cheaper, have a different set of outcomes, and tend to be more socioeconomically representative of society at large.