In my experience a fair number go to state schools for economic reasons.

Germany forbids home schooling. Did anyone see the recent case in which that Home School Legal Defense Foundation sponsored a lawsuit by a German fundamentalist Christian family who won political asylum in the US because they would not be allowed to home school in Germany. Big win for that home school foundation.
The home schooling strategy for US theocrats has been in the works for many decades. Christian Reconstructionists around R. K. Rushdoony, the conservative Presbyterian theocrat began advocating it in the later 1950's or 60's as a way of breeding a generation of ideological Christian theocrats. I think we are seeing the fruits of that strategy in our current political climate.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13