I get very irked in policy discussions when people fetishize private sector solutions. These people believe (I wish I could say "seem to believe") that a good or service delivered by a private entity is inherently better than one delivered by a public entity, who believe that a "market solution" is better because it is a market solution. This is wrong. The reason successful, capitalist economies mostly rely on market solutions is because they are mostly more efficient. That is, the use of market incentives in a lightly regulated economy generally leads to an allocation that produces the most goods that are most desired by most people.
And markets ARE extraordinary, When I used to travel on business, I would sometimes forget to bring enough dress shirts. But that was never a problem, because I could always just go buy a new one. Such a shirt consists of components, raw material and manufacturing value added from all over the world. Cotton from Egypt is converted to shirting in China that's combined with buttons from India and thread from Bangladesh in an assembly plant in Malaysia that is put into plastic bags made in Hong Kong, to be shipped off to the US. Then the shirts are stocked at a Nordstrom's in a mall in Topeka, waiting for me to pick one up. This incredibly complex supply chain is called into being almost entirely by the Invisible Hand power of market forces.
We are better off with a shirt production and distribution process that is not run by a group of central decision-maker determining how many shirts to make, and where to send them. This is how the Soviet economy was organized, and it worked out very badly, even aside from the corruption that inevitably results if you give some small group of decision-makers this kind of power.
But just as we know for sure command and control economies are a disaster, we also know there are instances where private markets don't work. The most obvious examples involve goods that must be bought collectively, like national defense services and equipment. Trying to work out a scheme to privatize national defense services would be a crazy pursuit of a private sector solution.
There are plenty of other examples, and there are even instances where it's not obviously crazy to use either public or private sector approaches. But the use of market mechanisms is one of the tools in a policy maker's kit, not an objective to be sought for its own sake.