I’ve told this story before on CC. A dear friend who was a great public school advocate; she and her husband went to state universities. They did well , were happy, and their first two kids did just fine in public schools. Both went to their large, well regarded flag ship state university.
But Kid3 was not like them it was rather clear that the chances of him getting through 4 years of Big State U with a degree were slim. A smaller Private was a better fit. A conclusion even the pro Public school parents made. For some kids, a private school simply is a better choice. Some people prefer them.
Of course, there are wide variances in private schools and public ones. There are huge private schools and smaller public ones. There are advantages that some schools have over others in academic offerings, access to classes, name recognition, culture, facilities , etc etc.
I have a cousin whose daughter finally came to the decision to go to he state flagship over a private school because the cost came down to the major difference. Just could not justify 3X the cost to go private. Had the money been no issue at all, it’s possible that the decision would have gone the other way. I agree the difference is not much and that with cost to them was not worth the advantages of the pricier school. In fact I see other advantages of the state school choice as well.
As a general rule, i prefer LACS which tend to be private because I like the more personal attention that students can get there. However , two of my kids who did go to relatively large state schools, the small departments of their majors really gave them a lot of nurturing and assistance.