You've posted twice about the supposed wonders of the NHS, but the reality doesn't seem to corroborate your claims. There are numerous reports about the massive financial crisis the NHS is facing. Evidently the problems are the worst they've been in a decade, resulting in significant layoffs and that 44% of hospitals will end the year in deficit. The fact that the things were bad only a decade ago seems to imply that the system has always had a problem with sustainability.
Sustainability seems to be a significant problem with socialized healthcare systems the world over. That's where the problems arise. Americans are hit with the cost of healthcare up front, Europeans pay for it indirectly via high taxes and other compromises. You'll likely be hit with a huge bill in the US, but at least if a doctor spots something of concern you'll be scheduled for tests the very next day. If they find a problem you can be in surgery the following week. In Europe you end up on waiting lists and hope things don't get worse before you get treatment. Unless you're wealthy, then you can pay for prompt care, which ironically causes the same economic divide people complain about in the US.
There are other more subtle problems I've personally observed in Europe in Asia. Doctors are overburdened and relatively underpaid. So I've found that they tend to gloss over issues and don't really spend enough time evaluating a patient's condition. These and many other problems are the sorts of things you only really start noticing when you've lived in a country for any length of time. I've noticed that immigrants to the US always complain about the cost of healthcare. Until they start noticing those subtle differences, the extra effort American doctors put into patient care, prompt treatment and a general sense that everything is handled more thoroughly.
At the end of the day, healthcare is a massively complex and expensive beast. I've yet to see an implementation that comes close to solving most critical issues.