The part you left out is that by paying less for services the state can tax less so that everyone will have more of their own money.
Mandating privatization isn't a good idea, as many have mentioned, their school district makes it work fine with employed staff. If employed staff are the cheapest way to go, why should a school board want to pay more for a private company to do it? Only if a private company can do it cheaper should this be an issue.
If ten lunch ladies got together and wanted to form their own company to provide meals for less than they were being paid with benefits and the cost of administration, the school board should go for it. If the lunch ladies can be more efficient, better purchasers, any profit (or loss) goes to them.