Only thing maintaining a standard of education across the country. If it weren't for the government, there would be for-profit private schools that have no accountability teaching our kids. Maybe a food corporation owns it and only sells burgers for lunch, and has a class on why its food is the best. Maybe a third of schools start teaching creationism. Maybe they refuse service to certain kinds of students. All of that becomes possible with corporate schools.
The other alternative, homeschooling, would be taken by anyone who couldn't afford the aforementioned private schools, and the only teachers would be your parents, who don't know nearly as much as a school system. There is also less opportunity for socialization for the students.
How would anyone be prepared for the real world in those two scenarios?
Also, public schools cannot, by definition, exist without being owned by the government. You might as well say corporate involvement is the reason McDonalds is messed up.