And herein lies the problem.
Parental involvement is arguably the single most important factor in educational performance among children. If you think about it, the teacher has the kids (in a group of thirty) for about thirty hours a week; the parents have them for well over a hundred. Helping your children with their homework and reading them bedtime stories are among the best things that you can do to help your children in school.
Parents who homeschool are almost by definition involved in their children's education, which is of course good. But that means that simply performing "better than average" is hardly an impressive achievement. A home-schooled child who is reading at grade level is underperforming; in a typical public school setting, a child with a high degree of parental involvement plus "normal" teaching would be expected to read above -- substantially above -- grade level. (This paper, which may unfortunately require a subscription, talks about the issue in some depth and provides some numbers.)
It also helps, demographically, that parents who homeschool tend to be those who can afford to homeschool (i.e. the low-performing low socioeconomic status families can't) and tend to be two-parent families (again, single working mothers typically can't afford the time.)
So any child who is in a position to be homeschooled should be doing substantially better than average even in an appallingly bad school district. Beth suggests that "homeschooled children average around the 80th percentile on standarized tests."
If their expected performance given all the other advantages that they have would put them at the 90th percentile, and instead they average at the 80th,.... I find it hard to see that as an accomplishment. And a parent who's child is "only" performing at the 60th percentile will probably not even realize the disservice they are doing to their kids.....
I can't respond properly at the moment (MadPuppy asleep on lap!), but CRITICALLY re-read your own post -- I find your post riddled with problems, both theoretical and practical.