Yes, there is no reason to believe those private school will not continue to send higher % students to top colleges. There are many families who can afford those tuitions, proven by those schools’ long WL and applicants.
Not all private schools are the same. There were private schools around my area that provided more nurturing environment for students with LD, and there were schools for wealthy families where they provided certain flexibilities, and there were schools that were more focused on academic. Both of my kids believed the education they received were better than their college. I for one do think K-12 education lays the foundation and probably more important than college.