Property taxes are certainly the mechanism by which wealth transfers from residents to public schools. They're a mechanism by which wealth transfers away from private schools.

But more relevantly, they are not a mechanism by which wealth transfers from residents into academic outcomes. It is non-controversial that wealth is correlated with academic outcomes, but it's not at all obvious that there is a causative link between them. Increasing the amount of money a school has does not in general improve the academic outcomes achieved by the students at those schools.