Public education has been exclusively controlled by statists (aka Ds), and it's been that way for many decades so if they are screwed up, you know exactly to blame. Anyway, it's true that the system isn't designed to teach children to think, they are taught to be drones, but it's not done to them for corporations benefit, that's just a coincidence. Children are turned into drones to facilitate government control and obedience to, and dependance on, The State.
If corporations ran schools, the kids would be drones, sure, but they'd also have the skills to be productive workers. Statists don't care about that, citizens being illiterate and obedient helps the DNC achieve their objectives.