A German couple moved to the U.S. years ago claiming discrimination at home since homeschooling is illegal there. The Service gave them marching orders and the SCOTUS refused to hear it. Then, another court ruled they could have asylum. There is an account of it in "Church and State" but I read it quickly and hope I have the procedural history correct. What basis would one have for such a claim of political asylum, that the German government has violated universal human rights? The Supremes' refusal might mean that the couple were members of a Protestant sect, in which case the New Majority on the Court wouldn't care about them much particularly. The magazine, published by Americans United (for Separation of Church and State) pointed out that the court found that Germany does not discriminate against any group, much less the German couple themselves, an indication home schooling is not illegal in Germany.
Not knowing a whole lot about home schooling, though knowing enough to make me certain I am against the practice on philosophical and political grounds just as I am with vouchers aiding public schools since, in the latter case, my tax dollars are going to, e.g. Catholic institutions, and right there with reading, writing, and arithmetic, you have Pauline gospel study. At home, one might think, things are worse. The walls are covered with dollar store Jesus paintings and the teacher-parent indoctrinates the child or children into evangelical Christianity whereby they grow up wondering why black people are not still slaves, believe Thomas Jefferson was a Christian, think that God created the universe all things in it (including dinosaurs) in six days about 5,000 years ago, and other positions on matters so foreign the use of reason and exercise of critical thinking these people might as well be living on the planet Kepler 62-e. Your experience of home school may be different and if so, set me straight.
I knew of several families back home in Central Colorado (which is assuredly NOT Colorado Springs), who home schooled their kids and sometimes those of neighbors. For the most part, this was to save the kids from spending hours each day in a bus on snowy mountain roads. Here in the Carolinas, most of the people that I know who home school do it for fundamentalist religious reasons, or so it seems. I recently met a couple here who home school their children for a variety of reasons, one of which is the pervasiveness of religiosity in the local public schools. I can attest to that. My young nephew went for two years to a very expensive Christian private school, not for the religion, but because of their high academic standard. To be sure, they did have Bible study, but they also at least exposed the students to other traditions. Moreover; the student body was quite diverse and the school just couldn't afford to alienate people who gave them a lot of money. When it became unaffordable for him to continue, he entered public school. Not only is academic rigor there not very, umm, rigorous, but the student body and faculty are 100% white and probably near that ratio Southern Baptist. I've visited the school a few times and have seen pictures of blue-eyed Jesus in most classrooms, and "IN GOD WE TRUST" prominently displayed in common areas. Of course this is entirely illegal, but to oppose it would put you in a minority of one in thousands, and that's a tough trip to lay on a little kid.
I can see how a secular (or black or Buddhist or...) parent wouldn't want their child "taught" in such circumstances, and so would choose alternative education. Judging by the homogeneity in that school, which doesn't reflect the area's demographics, I'd guess that there are many families that choose something else. I'm sure that a lot of them struggle to afford it while their taxes go to the (de facto religious) public schools and toward vouchers spent at the overtly religious private schools.
If I had a kid I doubt that I'd home school her. I think (and self-assessment is always accurate) that I'd have the ability to do a good job of it, but I also think that socialization in the larger community is very important to a child's development. It's also important to the development of the community. If we remove our own precious little burdens from local society by home schooling or sending them elsewhere, we deprive society of the diversity that it needs to flourish and promote clannish pooling.
I caught hell in kindergarten for preaching that Santa Claus was a scam, and later that God probably was too. That disapprobation came not just from my teachers but also and more importantly from my peers. I had a few followers and scores of detractors, and it taught us all a little about how societies work. I like to think that I (and self-assessment is...) moved the status-quo at least a little bit. When we choose to segregate those who can have influence by their diversity we create slums wherein divergent thought, and so eventually any thought, is discouraged.
At least you doubted God at an early age. It took me decades, though I think there was always a bit of a heretic in me. Your conclusions about home schooling, minus the snow, are similar to my own vis-a-vis home scholers' desire to inculcate religious "values."