That's not the problem. The problem is having government partially funding private companies.
Let the parents pay for private schools and the market will select schools that do the best compromise for their need. I've found some unverified results claiming that parents are more satisfied with Swedish independent school than public schools. If that's true, parents are still getting a better service than with the public offering.
I'm pro privatisation in general because, in my experience, government-run institutions waste more money and provide a worse service.
Of course if you get politicians underselling public assets to their friends, the loss on the assets is just going to be pocketed by politicians and you'll get a worse service.
I don't blame privatisation though, I blame the politicians.