It’s very difficult to make everything equal. Humans aren’t all equal. Ever hear that joke about, “What do you call a doctor who graduated last in his class? Doctor.” Same’s true for teachers and school administrators.
Even barring that, you have the problem that we live in a free nation. We don’t have the draft for teachers. We have to be able to offer people salaries that are competitive. We don’t have assigned stations for teachers. Is your school in the worst, most inbred crazy-ville of drunk wifebeaters? Guess who wants to voluntarily move there: No one. Even if the state is willing to pay the same amount of money per student no matter where they live, economics demands that you have to pay significantly more to get average quality employees to move nearby and be willing to work in that location. If you can’t, then the only people you are going to get are the ones who can’t get work anywhere else.
Are the kids and their parents particularly interested in education? Is there any reasonable expectation that doing better or worse in school will really open up any prospects in their future? Are the students going to ignore your teachers and destroy the furniture for the lolz? Are the teachers allowed to punish the students for bad behavior or are they stuck teaching to the ones who care?
Ultimately, you have to pay significantly more for a school in a failed community just to make it up to snuff with everywhere else. And if you do that, what are you going to accomplish? Now we have a bunch of Native Americans out in the wilderness who are competitive with the national average and a bunch of inner-city youth who can do math but still distrust our financial institutions and who are going to have to deal with potentially racist employers. And, unless we have raised the budget across the nation, in order to spend more in bad places, we will have had to have lowered the amount that we are spending to help kids with better prospects, more interest in further education, and who are geographically in the right place.
The reality is that in a racist world or at least a world that still suffers the after-effects of racism, a world where there are places where your best hope in life is to take over your pappy’s liquor shop, etc. it’s a ‘misuse’ of resources to try and make schools better. There’s a correlation between the quality of a school and the view of the parents, the local community, and the county and state governments on the value of the students from that place. And that’s just a hard one to fight, since it’s sort of like gravity. People don’t want to pay taxes, so they’ll demand that the government spend frugally. In turn, the government is going to prioritize spending and administrative effort where there’s a sense of value. Economics and real-world considerations play in from there.
Ultimately, the best research that I have seen is to suggest integrating communities and breaking up ones that aren’t very good. Mix poor kids in with middle class ones and have them go to the same schools. Keep the community and schools averaged out within the cities. Unfortunately, that’s going to be impossible for the countryside. Eventually, we’ll have a sufficient population density that, like Japan and Europe, there’s no such thing as “the sticks”. But that might take another century or two to achieve.