I think "good school district" is coded language for what you're making explicit—a district comprised of schools and teachers with necessary and adequate resources to provide "good/better/best" education.
I don't mean to detract from your point, because I think it is definitely key to education problems nationwide.
Edit: My statement about coded language did not include mention of the segregation and amplified economic disparity/inequality. It was not my intention to omit this as a means of saying it is irrelevant. It most certainly is. I was hasty in my paraphrasing. My apologies to rayiner for detracting from his very important point, which was not what I meant to do.