This is weird, because when people have a chance to choose (and the funding) they regularly come here for care.
Our healthcare may be skewed towards those who have the means to afford insurance (and this isn't quite true because emergent care must be treated), but it is the best in the world. We routinely do things that are science fiction in other countries with "enlightened" healthcare policies: deep brain stimulus implants, laser-etched re-mapping of nerve impulses across the heart (that bought my physician father a few extra years of life), CAT scans are routine, etc. Our physicians are also the best trained in the world. After having toured hospitals in the UK, only a fool or the near-indigent would rely on NHS in the UK — there's a reason why the Royals go to private clinics.
That's a bug, not a feature. American doctors know that they order too many scans; they know it's harming their patients; but they can't stop doing it because there's a false belief that "more scans == better care".
If you're in England and you need a cat scan you get a cat scan. They're not forbidden.
Honestly can't imagine anyone looks at the US and says that they want to emulate it.