The problem with that, and this is the same argument I've used against private school vouchers, is that the education of American children does much more than simply educate the children. It props up the infrastructure of the country. As Lectric said, if it wasn't required, then we would have more idiots out roaming around than we do now, and that would be bad for the country.
Of course, that doesn't help solve the problem. While I dislike the whole private school voucher thing, mostly because it doesn't actually help the children who would most benefit from it, maybe some sort of remuneration for good schoolwork would help. That is, give bonuses to teachers and principals whose students do well, which would encourage them to be more than babysitters.
I don't really know. I've never been in a school where learning didn't occur, but, then, I was always in the advanced classes. I suppose that the children who would really benefit are the seemingly average ones who would actually want to learn if they had the opportunity.
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Bitt Faulk