Good post, but it's looking at the thing the wrong way around. The bolded is exactly wrong: the need for services comes first, and then the taxation to pay for them. Government steps in - or, more accurately, is created to address - when there is a need to be met.
Most of the government functions listed these last few pages are pre-capitalist; the judicial system evolved from the need for someone dispensing justice - in most cases the headman of the tribe, originally, or the feudal lord later on, which evolved into a formalized legal system as communities grew bigger and more complex, and to include police and judges and the whole mess. The same goes for the post office, fire departments, armies for defense, and so on: there was a need, and people got together and created a government to fill the need. There literally was not a private entity with the ability to provide those services; any private entity with the scale to provide police or mail delivery for an entire country is a relatively recent development.
How does this relate to health care? There has been a growing sense over the last several decades that the private solution is not working; it's been getting progressively more expensive, inefficient, topheavy, and is simply failing to provide basic service to all. Yes, government regulations have played a role; that was clearly not the intent, but unintended consequences do happen. The default answer to a universal need that is not being met is a government service. Medicare and Medicaid may have distorted the private market, but the undeniable fact is, they work, and they work much more efficiently than their private counterparts. People will eventually come around to the idea that it may not be such a bad thing to have a system that works, cheaply and efficiently, despite however much propaganda the ones who benefit from the current system (insurance, pharma, private hospitals, etc.) generate.