I'm not scared of corporate exploitation, because I believe competition will make sure there is no room for it.
* Advertising: nothing wrong with it. However, it is costly for the manager of the school. The advertising would have to appeal to the parent, so it wouldn't be like the irrelevant advertisements you see about typical goods and services. Advertising would probably resemble a sedated political campaign: they would show their statistics and compare them with their competitors. Doing this would probably be the best way for schools to increase their market share. Private tuition companies already advertise, so I don't see what is wrong with it. The trend towards privatisation encourages individual responsibility, since consumers must think carefully about the goods they purchase. Thus, reform should be made gradually so that society can adapt to it.
* Company agenda: there would be no room for it in a competitive environment. Transparency would be an important aspect of a free-market education system, as those who choose to be transparent will have an advantage in the market. Those who waste time on company agenda and end up with kids doing worse on other "standard" subjects would be criticised, and parents would send their kids to more worthwhile schools. There may be some exceptions, but they cannot last forever without being exposed. In admitting this, I would always ask: is the cure (government regulation) better than the disease? I would say no. The disease will not get past the immune system (the free-market), while the "cure" limits market innovation and consumer choices.
School fees would increase overall, if there is going to be no subsidy system. If some sort of government funding should take place, it should not go to the schools directly: that will make the complacent. It should go to the consumers. This would be an "education voucher" system, where people would receive, say $5000 yearly, for example, to spend on a school. If the fees are lower than that, they will go into a fund for college, perhaps.
Propaganda within schools is worrying in both cases. Do you trust the corporations, or do you trust the government? I would trust the corporations. With the government, it is a monopoly. With the corporations, there is competition. The free-market will stamp it out, if it desires to.