Are There Any Conservative Government Schools? . . .

[redcliffsw]

If there is to be any state involvement in education, it must be limited to the state level. The federal government has been given no such authority by its Constitution. But this is only because every state has a provision in its constitution for the operation of K-12 schools, colleges, and universities, not because it is libertarian for the states to do so.
-Laurence Vance

Read on:
https://www.lewrockwell.com/2017/08/laurence-m-vance/are-any-of-them-libertarian/

He's right.