Indeed, not everything done elsewhere could work exactly the same as in the US, but there is a very widespread sentiment among Americans that America is a snowflake in every way, which kinda prevents the population to look elsewhere for ideas.
America is one of a kind, no doubt about it, but Americans are humans, so much so that a very large portion of your population immigrated from everywhere else within the last 50 years, which means that policies that worked somewhere else could very well work in the US too.
And again, healthcare is a good example of that. Supply and demand. Supply and demand. The "problem" in your rhetoric is that... you see health as a product that can be bought. Although it does have a price, this price is not a choice you have, you either pay it in money or in years of your life. What we have for "free" or included in our taxes in Canada are things that everybody needs, all the time, no matter the age. Healthcare, insurance, basic legal assistance, electricity, water, etc.
Have you ever seen someone who genuinely could live a normal life, today, without spending half his days producing it, not needing electricity?
Have you ever seen someone who never, ever, ever needed medical assistance, at anytime in his life?
I won't ask if you've ever seen someone who didn't need water...
Now, the point is not for it to be free, because some feel when something is free, people don't see the value of it, but the point if for it to be affordable, available, and not inflated by a need to make profit.
What about a level of income, level A, you pay 50$ to see a doctor, level B, 20$, level C, it's free.
Level A, 150$ for a kidney stone removal, level B, 75$, level C, 10$.
Level A, 5¢ a kw/h for electricity, level B, 2¢, level C, 1¢.
Level A, 5000$ a year for tuition, level B, 2000$, level C, it's free.
Doesn't have to be free, just has to be affordable, comprehensive. The system I just quickly explained takes into account your ability to pay, what it represents for you, which prevents over usage like some fear, without preventing the poor from using, like it's currently the case, and it does bring in revenue for the state, which, usually, would go back in the system to help improve it. Keep in mind it's a question of mindset, such a system in the US would be under such scrutiny by the public that they would make sure there never is a misstep, which I believe would make it a good thing.