"The teachers spend most of their time with the stupid kids (I am not politically correct) and subsequently can't challenge the smarter kids."
I'm not politically correct, either. I view political correctness as an ideological evil. I think it's possible to remain polite while using terminology that is both descriptive and accurate.
Teachers have to teach to the lowest common denominator. There is no other way that I'm aware of for one person to attempt to teach a group of 20-30 children. I think that the idea that one person can effectively teach 20-30 same aged children borders on the idiotic, but that's the paradigm that the government schools as well as the private schools are operating on. The big difference in academics between the private and government schools in my view is that the private schools are generally teaching to higher common denominator. If you think about it, the really bright kids in the private schools are being academically shortchanged as well, although not to the same extent that they would be in the government schools.
As for your wife's experience with home education. Are you sure that what she's being exposed to are not simply truants who are invoking the words "home school" as a sort of talisman to ward off the truant officer? I think that's a problem, and one that is being exacerbated by government school administrators who are being pressured to deliver better results. One way to improve the numbers is to suggest to problem kids that they simply leave the government school to be "homeschooled." The kids in question aren't going to receive any further education. There's even a term for these kids; it's called being a "pushout."
Playing this sort of game is a win-win scenario for the government schools. They get rid of the problem kids and/or their families, their statistics improve, and they have some convenient homeschooling failures that they can point to. The kids are happy, too. At least until they realize sometime later that they're going to spend their lives on the economic trashheap.