> Another part is the fact that quality education is insanely high-priced because a parent has to pay for the public and the private system concurrently. This pressure pushes private tuitions upward and makes the private schools more exclusive because they can't take on kids below certain income thresholds at all.

How does that hurt public schools? I would assume that would help public schools. Because instead of the top 50% of kids (e.g.) going to private schools, now only the top 10% of kids go to private schools. Thus public schools are filled with smarter kids.