Politics

The US has basically all 4 major healthcare insurance systems in a single country.

The Beveridge model, used in the UK for its National Health Service, is essentially socialized medicine where the government literally owns the hospitals/clinics and employs the doctors and other professionals who work within that system. It exists in the U.S., too, in the Veterans Health Administration system, and the military's own hospitals, plus a few smaller systems like the Indian Health Service.

The Bismarck model, common in much of continental Europe, is essentially an "all payer" system where private insurance can still exist, but where all the insurers are paying the providers the same prices for services. Providers are private, but the highly regulated price structure means that private providers can't just demand their own prices (lest they get cut out of the insurance system entirely). Insurers can be private, too, but all plans must offer specific features, in a way that ends up pushing the pricing and coverage to be fairly uniform throughout the system. This exists in the U.S. in the employer-provided health insurance system, or the "Obamacare" ACA exchanges, where most states regulate what insurance coverage there can be, what prices they can charge, and then all the providers and insurers negotiate prices that end up looking pretty similar. Realistically, someone who gets Aetna through their employer doesn't have all that different of an experience from Blue Cross Blue Shield or Cigna or United.

The Medicare model, or single payer model, basically puts everyone on one public insurance plan and has that insurance system negotiate prices with providers as a monopsony. Doctors and other providers don't have much room to just opt out of the system, because in a society where everyone has insurance for no or low out of pocket expenses, doctors won't be able to charge significant out of pocket expenses for normal services. It's what Canada has, and what the United States has for everyone over the age of 65, as well as everyone under the age of 18, and most people below the poverty line.

The chaotic market-driven model, where patients and providers essentially shop around and negotiate one-off pricing for services, is basically what remains for anyone not covered by the three models above. It might be how markets work for most other stuff in the western world, but among developed nations only the U.S. uses it in a significant way for health care markets.

Single payer, or Medicare for All, is at least something that one can envision for the United States, but I think it's far more likely we end up with something like the German/Swiss model, which probably would be the easiest transition among the 3 major universal health care models. One disadvantage is that it doesn't really look like what we see in other English-speaking countries (Canada's single payer, UK's socialized medicine), so there aren't as many people explicitly calling on the U.S. to adopt models already implemented in other countries.