Have you actualy checked the school funding differences in your local city? The city wide funds around here go into one school system. I thought that was common?
I've looked through the budget spreadsheets for the Charlotte, NC school system. Schools in areas with more welfare recipents receive an even higher funding level and more teachers. These schools still may still be terrible, but relative funding between schools is not the problem.
I don't know the specifics of e.g. North Carolina, but note that higher average student funding != higher median student funding.
This is because often low-income schools have very high amounts of students with disabilities. Students with very harsh disabilities can require one-on-one or few-on-one supervision. This means that they can eat up a substantial portion of a school's budget, leaving most students with significantly less, even if the school receives nominally more funding.
Again, not sure if that's the story in NC-- just that the story of funding is a bit more complex than the average amount per student.
I've looked through the budget spreadsheets for the Charlotte, NC school system. Schools in areas with more welfare recipents receive an even higher funding level and more teachers. These schools still may still be terrible, but relative funding between schools is not the problem.