Right, implicit but unsaid was the thought that the federal gov't could cover that funding gap so that all schools got the same budget regardless of the local conditions. Of course given the political forces that created the current local conditions in the first place, that's probably unlikely too.

If you make the federal government cover all equalization you'll find rich areas lowering their property taxes.

Other nations handle education at state or federal level from the start. If you want a federal equalization you will want it to come with a admin union as well.

Even state governments could solve the funding gap between schools.