In this country is some discussion if home schooling should be forbidden. I think that's a good idea - I abhor monocultures and a family that isolates the children is a monoculture. The quality of the schooling might be an uncertainty...
and at that point I realized that I can't think of a point in favour of homeschooling. So who has experience with home schooling and can tell about the pros and cons?
I homeschool. There is a large community of homeschoolers. Some religious, some not. I have not met any religious families that are hardcore about it. They tend to teach their kids all the normal things but also include religious studies.
I understand your concern but making homeschooling illegal is not the answer. The laws vary from State to state. Some are incredibly stringent and others are incredibly lax. I live in one of the most lax states. Everyone I know (hundreds of parents) still takes it very seriously.
Having more options is highly preferable to having no options and having your life dictated for you and your children. Yes, some kids are probably done a disservice by homeschool. More are done a disservice by public school. You decide what is right for you and your kids, I will decide what is best for me and mine.