Your last sentence negates the two prior. But more than that, you completely ignore the elephant in the room. Profit.
Private healthcare, private education, private prisons, private military. The more we privatize social goods (those that everyone needs) the more they cost and the worse the quality will be. You think there is a lot of bureaucracy in government offices? Dude, take a look at a private health insurer. They have whole divisions devoted to finding ways to not pay for your healthcare.
Private education has to provide profit to its owners as part of its business plan. That profit is money that is not being spent to actually educate people. It is wasted overhead in something that every society needs.
Private prisons and miliatary (contractors) are even worse. They have an incentive to lobby the government for more prisoners and war because that is how their business profits. How sick is it to have a company pushing for more people in prison and more death and dismemberment because instead of necessary evil, more prisoners and wars become goals to be achieved?
Belgium is a wonderful country in part because they understand that the word society has the same roots as social and socialism. The more you push social goods (as opposed to private goods like dishwashers and cars) into private hands, the worse your society will be.