Here's problem with homeschooling for a year, learned the hard way at our house.
Schools won't accept courses that aren't taught by accredited institutions. I taught algebra 2 to my son last year because we didn't like the online courses we found. When he went to the local high school this year, they wouldn't give him credit for the course or for another course he did with me. So now he's behind on credits. This sounds bad, but he it could have been much worse. His counselor initially told us that they might make him repeat algebra 2! Then there was a bit of a mixup, and in its midst, he just got enrolled in precalculus. We kept our mouths shut. I should add that what I taught was way more rigorous that the local high school's course.
Local middle schools (public/private) have said the same thing about me teaching algebra to my daughter, and I'm only trying to persuade them to let her skip pre-algebra and just do their algebra course. In their minds, there is a procedure, and it must be followed. Anything off the path doesn't count.
What I've learned is that the schools can be resistant even to testing out of a course. It sounds so reasonable to just test the kid, but my impression is that they don't see things that way. If you aren't accredited, they don't trust what you've taught or what the kid has done, even if you used their book and even if the kid got a very high score on a standardized test. If you don't do all the work in front of them, it doesn't count.
I know, this is nuts.
I disagree with the policies you have mentioned but their existence is easy to explain:
(1) The gaps in lifetime earnings between people with people with BA's, high school diplomas, and those with no high school diploma are enormous. It would be great if high-end employers recognized the math and programming schools that my eldest child is developing outside of school, without his getting a B.S. degree, but I see little sign this is happening.
(2) Given (1), parents, students, and taxpayers feel compelled to spend enormous amounts on education.
(3) Don't expect the people making comfortable livings granting the credentials to be receptive to alternative ways of certifying what has been learned. That could put some of them out of work.
As Upton Sinclair said, "It is difficult to get a man to understand something, when his salary depends upon his not understanding it!".
