Ever work in an over-worked bureaucracy? Things just don't work that way. Bureaucracies will tend to focus only on the egregious problems, and tend to do a cursory job otherwise. Furthermore, it's trivial to establish a deferential standard of review in the procedures. Any second-year law student can do it.
Overall, though, the stats show that they do better than public schools. For now that should give guidance on how to proceed.
The way you cite those statistics is fallacious. Statistical averages tell us just that - the average. It counter-balances the low-performers with the high-performers. The distribution curve of the scores almost certainly shows that there are high-performers that would do well in any half-way decent school, middle-level performers who are thriving under individualized attention, and low-end performers who may struggle in any environment, or whose parents have no business homeschooling. An average gives no information about how many fall in each category.
On the other hand, the stats do tell us one thing - homeschooling does work and should be a viable option for some. Anything beyond that is conjecture.
"Ever work in an over-worked bureaucracy? Things just don't work that way. Bureaucracies will tend to focus only on the egregious problems, and tend to do a cursory job otherwise."
Show me a situation where the gov't has returned the power of choice to the electorate because it was too much trouble to maintain or do the work. IOW, show me a bureacracy that got smaller because the bureaucrats said some of their function was not necessary.
"Furthermore, it's trivial to establish a deferential standard of review in the procedures. "
I wasn't arguing that establishing a deferential review would be trivial -- it's just that there is no guarantee that it would remain deferential. Gov't grows and grows and grows like a weed. Since we are talking about education, look at the Dept. of Education. It's the perfect example.
"The way you cite those statistics is fallacious. "
No, it's just that the average can tell alot. If the average homeschooler does better than the average public school child then that tells you that the system is overall better. The distribution might be narrow, wide, or skewed one way or another, but to have an average that is centered that much higher is very significant.