The majority of the far right who home school are installing robotic hive thought in their little schoolers.
I don't care if you teach Creationism or ID as long as your student can also competently and objectively discuss Darwin and evolution, able to make the argument for it.
Same way with the Civil War, for example.
If home schooling is not instilling critical thinking principles along with parental propaganda, then a case for state regulation has certainly been made.
Robotic hive thought can only be achieved when the children are herded together in public schools. Hives don't work with only one worker bee.
Fail logic on your premise. Of course a hive (a home) can have one school bee.
And don't try to ignore critical thinking principles as the basis for learning.
If any school does that, good, whether private, public, or home.
And if not, shut it down and exile the parents/teachers to coastal Alabama to make their living on the beaches.