In some cases, no. Some parents aren't qualified at all to direct their children's education. And, making a blanket statement of "parent's aren't qualified to direct their children's education" is also wrong. Some parents ARE qualified, some aren't.
I really don't think that a flat earth society parent is qualified to educate their child, because their bias and beliefs will filter through the teaching (the world is round by the way) and the child will end up with a sub-par education. Same thing for parents who believe that the Earth is only 6,000 years old and that dinosaurs and man lived together at one time. Some parents either don't know because they never had the chance to learn the reality of things, or they choose to ignore reality because it doesn't fit in with their beliefs. Yes, those are extreme examples, but they exist. And, there are other biases that some adults have that can filter into a child's education because the parents believe that anything outside of THEIR knowledge base can be dangerous or threatening.
Me? I went to public school in Montana, and was grateful for a pretty decent education, but that was back when schools actually thought you should learn something (graduated in 1982). Schools today? While there are some out there that are still pretty good, I can tell you that there are quite a few that aren't, and I can understand why some parents would want their kids to learn in a different environment. I remember my first learning about a crappy school was when I compared my education with my ex-wife's education when we were first married. I was shocked, because the stuff she was learning in high school was stuff that I'd already learned by 8th grade, and the stuff I was doing in high school was far advanced to what her education was. But, that's because we grew up in different areas of the country.
Yeah, there is a problem with education today, and I don't really know what the solution would be, but giving parents who never graduated HS access to a 6,000/year scholarship to direct their children's education doesn't sound like a solution to the problem.