Robert Frank says the positional nature of school quality helped fuel the housing boom, making it difficult for families to borrow responsibly when purchasing a home:

But what works for any individual family does not work for society as a whole. The problem is that a "good" school is a relative concept: It is one that is better than other schools in the same area. When we all bid for houses in better school districts, we merely bid up the prices of those houses.[...]
The result was a painful dilemma for any family determined not to borrow beyond its means. No one would fault a middle-income family for aspiring to send its children to schools of at least average quality. (How could a family aspire to less?) But if a family stood by while others exploited more liberal credit terms, it would consign its children to below-average schools. Even financially conservative families might have reluctantly concluded that their best option was to borrow up.

I don't think it makes sense to view the quality of local public schools as a pure positional good (there would be a real difference between a society where the graduates of even the worst high school all had basic reading and math skills and the society we actually live in) but there clearly is some positional component here and I think Frank's analysis explains at least some of what we've seen.