You haven't heard of the San Francisco mother who (with a mere high school education) taught her kids while living in her car? They scored 1600 on the SAT.
Frankly, there are so many children graduating from pubelick high skewels incapable of reading at a 4th grade level that I cannot imagine a parent doing worse simply for lack of an education. Further, that parent, if committed to the task, will use the opportunity of educating their children to correct the faults in their own schooling. I have seen it many times and society thus benefits two ways.
I will answer the rest of your ill-consderations directly however (unlike you), and say that there are probably parents who are incapable of teaching their kids. The good news for you is that they are, as a group, not inclined to teach their kids at home. For those who have kids that have been rejected by the public schools and don't desire to teach them at home, I think allowing the state to judge and regulate the rest of home schooling parents too high a price to pay when that populaiton will without doubt end up a customer of the system regulated or not.
Thus, not have you failed to establish a legal Constitutional claim to COMPULSORY public education to Mr. o, you haven't shown me how the measures you advocate could deliver the outcome you envision.
This is a total misunderstanding of what happens in home education. By then the child is usually able to read the instructions and teach themselves,they no longer want the parent sitting over him constantly. If a parent does not understand a concept or can not help the child understand a subject when the child runs across something he can not figure out, there are other avenues of help availiable to him/her. I had a terrible time trying to teach Chemistry at home, I never found that it worked well. Instead a woman in our community who was a medical researcher at a local hospital puts on a class every year to teach chemistry. My child went and took chemistry at the local community college getting credit for both high school and college at the same time.
My husband helps other homeschoolers whose parents are not strong in math when their child has a problem in math. There are many ways to work around problems, we end up with some rather creative ideas to solve what problems we encounter.