I seriously doubt the premise of having nothing but corporate schools to choose from, but OK, if Dick Cheney became Secretary of Education...
Seriously, I disagree with those who think they would save any money compared to public schooling. Look at private schools - almost all spend more per pupil than public schools do, and the best spend much more. It defeats the argument that you can't improve education by throwing money at it, when private schools do.
Some think that parochial schools are cheaper than public schools, which often seems true, but parochial schools are funded not only directly by tuition, but indirectly by the church, which of course is funded by its parishioners and the investments made possible by them. They may also receive funding from the mother church, which is interested in more adherents.
Meanwhile the purpose of a corporation is to make a profit. If the purpose was to obtain skilled workers, most non-service corporations would be likely to obtain them from other countries that paid for their worker's education. If they managed to create a monopoly on education and their purpose was to profit from it, they would extract every dollar they could from parents, educate students to meet the corporation's needs and brainwash them with corporate propaganda. Anyone who thinks that large corporations have anyone's interests at heart but their own should either have their head examined, check out an overseas sweatshop or read history.
As for for-profit schooling that is not aligned with industry, we've already tried it in the U.S. with the Edison Schools, and that went over swimmingly. They ran out of money trying to compete with the public schools while earing a profit. Newt Gingrich used to tout the Edison Schools often in the 1990's as the school of the future, but went silent on the subject once things went sour.
Personally, if the U.S. ever switched wholesale to corporate schooling I would make every effort to move my family to a more enlightened country.