If you were a conservative, you wouldn't want a school board, at least not a public one.
Why not? Public schools have a long history in this country, with even Thomas Jefferson being a proponent. The Land Ordinance of 1785 specified one acre for a public school in each township, and about half of the founding states had public education in their constitutions.
Education being best managed locally, our problems began when the states started exerting more control over districts and combining them for easier top-down management. Then the federal government got involved, making things even worse.