Well, let's be factual.
Big city public school schooling is overly expensive, poorly run, indoctrinating instead of educating and, dare I say it, dangerous.
Now, if you want to dispute that statement with facts, have at it.
You stated it was also outside the big cities in some states.......
I grew up in NYC, I know about big city schools, public and private. Trouble is not confined to public schools, be they in big cities or rural communities.
Where I live, which is very rural, the good kids, academically and socially, do not want to go to the only private HS in the area because it is a haven for the bad kids and the gangs.