> And obviously, particularly in a hierarchical capitalist system, it would not be possible for every family to afford tuition fees for private schooling, which would very significantly disadvantage a large proportion of youth.
I stopped reading at this point. Up to here your post was riddled with errors, but once you make the completely unjustified jump from "some people wouldn't be able to afford tuition" to "obviously that would be a large proportion," I don't see much point in reading further.
For the record there are lots of options besides the for-profit corporate organization you're imagining, which capitalist ideologues entirely support, and many ways to provide education to even the poorest people without violating anyone's property rights.
There's a great book on real world private schools serving the poor and how they stack up to the real world implementation of public schools in those areas: The Beautiful Tree: A Personal Journey Into How the World's Poorest People are Educating Themselves.
Yes, state would not educate anybody under capitalism. It is not state's job. But you are not providing any evidence or justification that people would go uneducated. It is quite clear in today's america that many people value education so much and consider the government one so abhorrent that they are willing to pay for it twice. There is also no reason to think that the poorest would not want to get educated as is documented nicely for example here.
There are very few things that capitalism would claim it does equally and education is definitely not one of them and that is a good thing.
What country has private education industry?
That sounds like a statist system though, where kids are forced into government schools and parents and non-parents are forced into paying for them and only those who can afford both to pay for government school and an expensive private school, expensive because government has crowded out cheap private schools, can go to private school. And then there’s the lack of innovation in pedagogy and curriculum and teaching materials that poor and rich students can’t benefit from.
https://www.amazon.com/Beautiful-Tree-Personal-Educating-Themselves/dp/1939709121/ref=nodl_
I dropped these two links in some comments below, but it's an inciteful discussion about private schools in areas that are way way way poorer thank Louisville. Full disclosure though, I'm a Libertarian and think the government should in no way be trusted with something as important as our children's education.
https://www.econtalk.org/james-tooley-on-private-schools-for-the-poor-and-the-beautiful-tree/
https://www.amazon.com/Beautiful-Tree-Personal-Educating-Themselves/dp/1939709121
> what makes the author think that private schools spend any less on administrators?
I've seen some data on it. I'll try to find it. Though I'd be seriously surprised if private schools are going through the exact same nature of administrative expansion as public schools.
> where does this assumption that private schools would perform better with the same resources/students come from?
James Tooley's work on low-cost private education around the world in country after country has found that private education outlets, even with LESS resources than govt schools, consistently and significantly out-performed those govt schools.
> why the heck does it keep bemoaning a "government monopoly on education" when private schooling is literally everywhere
In any other industry, 90% marketshare would be considered a monopoly. In the US, less than 10% of students attend private schools.