Home schooling isn't reliant on what the parents know or don't know. Almost all home schoolers use materials from outside sources, some free some not, but there are numerous curriculums available and they are not unstructured do what you want programs. There are a lot of networks for home schoolers as well.
My thought about the home schooling not being a solution was more because once an adult has no critical thinking skills themselves because of their public school education, then they also have lost the ability to see what public education is doing to their kids as well, and that their kids would benefit from getting an education from some other place than the public school system. That situation is what I see as hard to get turned around once we have gotten ourselves to that state.