Is it possible that the federal government could set up an educational system that would equally benefit each state?
It would be possible for the federal government to set up such a system, but it would be very difficult to do it in such a way that all states would feel that it was both fair and beneficial.
First, any system that is set up by the federal government will be resisted to some degree by the states. States in our system of federalism have certain areas of policy that are supposed to be their domain. Education is one of them. As we have seen from the No Child Left Behind law, states simply do not like being told what to do in education by the federal government.
It would be possible to set up a system that would (at least in terms of dollars) help all states equally. The federal government could set up a formula where it looks at the amount of funding that each state provides to education. It could then provide each state with grants that were equal to a certain percentage of what each state spends. This would help each state equally because each would get a grant of the same percent of its spending on education.
While this would help each state equally in objective terms, it is likely that states would not see it this way. Poorer states that could afford to spend less on education would not like the fact that richer states were getting more money in absolute terms.
So, it would be possible, but it is unlikely that all states would perceive it as fair or as beneficial.