The evidence IS cold cut and clear: government management of Health Care (disguised as the phrase single-payer) results in higher costs for procedures and medicines, shortages of even the most basic of supplies like antiseptic and bandages, dirty facilities, and patients dying in the hallways as they await service.
There are no taxes levied in order to prove food and shelter, but yet the market provides you food to eat and an apartment to live in. Taxes are not needed, not even for “infrastructure”. By that I assume you mean roads, since most other infrastructure in varying degrees is already built by the private sector (cell towers, power lines, shipping service, security service, arbitration service, etc.). Even public road construction is sometimes contracted out to private companies. In some places, many roads and streets are already entirely privately constructed and maintained, even some utility services; in residential subdivisions, for example.
I don’t have to prove ‘who will do X without the government’, because the market already shows that it can. And it would do more, if allowed to.
What?! You can't be serious. France, Germany, Finland, Iceland, Israel and the like have better health care than the US and they get it cheaper. And I assure you they all have access to cleaning supplies in the hospitals there and they know how to use them ;) And are well stocked on bandages...
It doesn't. There are many cases in history where you find that left to the market, things are not taken care of and the government needs to step in with regulation and often to take the project upon itself. Look at the history of the London sewage system for instance and tell me how well the market handled the problem and how the problem was solved. Could it have been solved in any other way and what would the incentive be for the hypothetical private investor who could have solved it? So yeah, you have to show that this type of counter-examples to your thesis are somehow invalid.
Again, you didn't explain how the market could create a world wide web. If things were left to the market, different companies would have the incentive to create their own local networks which they would control and charge for all the content. We see this even not as large telecommunications companies pushing against net neutrality. The market has not way to preserve net neutrality and thus the free market without government regulation is very likely to destroy the internet that we know, love and almost take for granted. And yes, you have to show that this is not a valid counter-example.
And the most important thing that the market itself can't do - enforce contracts, protect intellectual property and provide justice. I keep asking you how the market would provide them and you keep dodging the question and move on to talk about food and shelter. If you look at the market you will see that business are happy to steal intellectual property if they can, so you need a way to stop them so developing new technologies would still be a worthwhile investment. If you want a thriving economy you need a level of stability and security and if contracts mean nothing, you are not going to have that. Same goes with crime. High rates of robbery and theft don't go well with a booming economy.
If the market was in fact a panacea, it would have already fixed all the problems, wouldn't it?
What is stopping the market from fixing health care right now? Private clinics and private insurance are not illegal, right? If there was a winning market driven formula there, why isn't the market jumping on it? What are the regulations that are stopping it from working?
The London sewer system existed before that time, and it was privately owned by several different companies but they were hampered by rules from local government.
And yes, competition in health care is Highly limited in the US. In every case, when a third party pays the bill (a single payer system/medicare or one with required coverage by private insurers) the cost skyrocket, while the prices for less regulated procedures go down. Consider lasik surgery, not normally covered by insurance but the cost has come down dramatically in just a few years. The American Medical Association also is a huge barrier to entry in the medical field and basically acts as an occupational cartel. Have you heard of a Certificate of Need? It's what you have to get signed off on by local existing medical providers, before you can open you own practice. Spoiler alert, they dont. This is some of what is stopping the market from serving consumers in the health care industry that desperately need more choice and less government.
And why are single-payer systems doing so much better outside the US?
https://mises.org/library/socialized-healthcare-vs-laws-economics