That's a rather poor example - healthcare is an exceptionally heavily-regulated industry. There's an argument to be made that many of the ills in the industry are a result of over-regulation.
That an argument can be made doesn't imply it's a good one, or that anybody should pay it any heed.
Most of the ills in the health industry stem from the fact that providers--insurers and direct providers alike--have a profit motive rather than a "provide healthcare" motive, because their market is entirely captive and literally without any (real) choice.
Most tire shops have a profit motive rather than a "provide tires" motive. It's true that tire customers aren't "captive", but I don't understand which sense of that word you mean to apply in a relevant way to health care consumers.
You don't understand how health care consumers are captive? Health care is literally something human beings cannot live without. The quality and cost of the care is far less important than its availability, because it's literally a matter of being healthy and surviving, or becoming or continuing to be ill, deteriorating and then dying. Healthcare consumers, in other words, don't have real choices in where and how they obtain care. This isn't the case with tires (or almost any other non-essential good or service).
As a Canadian living in the US, I'd have to say it works a lot better than up north. I realize that's probably heresy for a lot of people, however, it's hard to stomach seeing your parents having to wait multiple years to get in to see a doctor. Particularly when they have debilitating health issues.
That said, I'm not sure what the right answer is; I want everyone to have access to good health care. I'm not sure I need to be able to get in to have an MRI in a day or two like I can here, however it would be nice if my mother could have one without waiting for two years.
Having lived and worked in the health care industry in both countries, I'll have to respectively disagree. I can see how your personal experience must be very frustrating, and I'm not attempting to belittle that.
However on the whole the Canadian system is better at delivering the health care that is needed. Overall, it works better for more people, more of the time, and much more efficiently (i.e. cost effectively). The latter point means that sometimes people with non-critical issues have to wait -- usually not very long notwithstanding the stories people sometimes focus on (the dramatic failure modes of the US system are much, much worse).
That being said, if you a) have the right insurance, b) live in the right state, c) have money, and d) live in the right part (typically urban) of the state -- you can get very good care very quickly in the US. Unfortunately that leaves out an awful lot of people.
You can just cherry pick examples unless you can explain how it's analogous. For example, healthcare suffers from natural monopolies to an extent. Hospitals don't really have to compete with each other, and it's really difficult to build a new hospital. The same principle applies to telecommunications.
On the other hand, healthcare is heavily regulated and hardly a free market, so it's pretty terrible comparison in that aspect.
Look at "US Unfunded Liabilities" towards the bottom. The US is drowning in debt, due to promises made... Or promises soon to be broken. It's laughable to suggest the free market is at work in the medical industry.