Not exactly so simple. For one, like another commenter mentioned, funds are provided by the federal government specifically to level these differences out, but that's all it is, money. The administration of those funds is carried out at the lowest levels of government, with little to no accountability standards from higher up (obviously we've had reform attempts on this like NCLB).

The differences arising from living in a poorer district vs a richer district have more to do with factors outside of school, like I said. It has to do with the home environments provided by parents who are often much poorer and thus less able to provide care and tutoring outside of school. Less access to role models that can guide the way to getting to college and upward mobility. As our country's economy becomes increasingly competitive, these disadvantages ossify socioeconomic statuses for people and their offspring.

Obviously, more oversight of funds is a good thing, but it really isn't a lack of money that leads to these problems (for the most part).

Edit: Also, a poorer district usually has lower cost of living to weigh against lower property taxes.

No. Even though school governance Halle s mostly at the local level, half of school funding comes from state and federal sources, to even out disparities in funding. This is the typical model pretty much in every federal country.

It often doesn't really work that way though, especially if you contrast suburban and urban school systems. It's not at all uncommon for urban systems with poor educational outcomes on average to outspend on a per-student basis middle-class suburbs. So it's not as simple as throwing money at the problem.

Bingo. Schools in the US are usually funded by property taxes, which leads to all the effects you just named.