We should, because it's in our Constitution as a State function, not delegated to political subdivisions:

Article 7, § 1. Public Education

The legislature shall by general law establish and maintain a system of public schools open to all children of the State, and may provide for other public educational institutions. Schools and institutions so established shall be free from sectarian control. No money shall be paid from public funds for the direct benefit of any religious or other private educational institution.