One thing that's really common is for parents to try it when they feel that the local system is failing their kids in some way and the family economics supporting are acceptable.
There are also many permutations - it wasn't uncommon when I was younger for parents to do it through middle school, but have their kids attend high school because they felt that it was the point where socialization became important in a way that couldn't be handled effectively with home school.
Obviously there's a huge range of efficacy, too.
That said, I think you have to ask why are charter schools and vouchers (not just home school) becoming even more fashionable despite there being little to no evidence that they generate any broad improvements in the base level of education in the population at large? And a lot of it is because society has gotten more and more zero sum and it's going to increasingly self cannibalize.
Which is not that far off from the writer's premise.