I don't think that's it. School sucks, and my school was 11 years of pure hell, I don't argue that, but locking a child with a parent and giving parents even more control over their life is not a solution
Can there be good homeschooling you think? I would think you'd want to prevent the horror stories while not preventing people from providing their own superior option to public school.
Unless parents really go out of their way to prove otherwise, parental relationships are by default inherently adversary. So while I can assume the possibility of good homeschooling, that's one to one thousand chance. If parents are actually good, if they still find ways for a child to socialize and see worldviews different from parental ones, and if they can ensure education on a level compatible to public school on all topics
Yeah, I believe parents most of the time want not what the best for child, but what's best for the image of the child they've built, and what's the best for their own ego to convince themselves that "I'm such a good parent!"