I mean, no, most Americans are just upset about cost-sharing, most providers in the United States are pretty good and have pretty good facilities and equipments.
You can have systems that are mostly privatized (cough, France) that are better regulated than the United States, but that'd mean doctors would get paid less money & upper class folks would likely get worse care
I agree that upper-class folks' experience would change in ways that would generate loud protests. But the biggest anger points likely wouldn't involve quality of care. Instead, we'd hear shouting about:
providers' increased emphasis on cost-effective care. (You don't need an MRI because there's nothing in your symptoms that warrants it.) Right now, there's a lot of overtreatment in the U.S. medical system, catering to patients' desire to get big workups.
scaling back of today's concierge-level ambiance, with fancy chairs, skyline views, etc.
It’s not just happening in the US. What goes on in the US is very influential elsewhere, and both patients and staff get pulled into the vortex of over-testing. And then to top it off, sometimes they are correct and they did need the test.
I think has more to do with a combination of overtreating results in higher income and fear of malpractice suits if you undertreat.
CoNs are something lobbied for by hospitals. If you want to open a new hospital or healthcare facility in an area, you need to apply for a certificate of need, which allows/asks existing hospitals if they think there is a need for your facility, to avoid "overservice" (lol, okay) of an area.
Diagnostic imaging companies - each of the big ones (Siemens, GE, Philips) offer in house financing for MRI, CT, etc., that they advertise to physicians. They also all offer specialist consulting help to facilitate you getting a CoN for your facility. Hell, they all also well help you find other physicians in your area who'd like to go in on setting up a DI facility (and will assist with spinning up the practice).
And then we find that physicians who own a DI practice (or a share in one) refer their patients to diagnostic imaging at rates several standard deviations above other physicians, and at rates that are "statistically improbable" when correlated to underlying ICD-10 diagnostic codes.
Upton Sinclair comes to mind ("It is difficult to get a man to understand something, when his salary depends on his not understanding it").