The EU and Japan, South Korea, Hong Kong, Bahrain, Brunei, Australia, and New Zealand. It works all over the world. Research on the US system accords with the overwhelming evidence from all around: it would work.
> eg, I'm not sure how they're connected ... medical research
Let's clarify. The repugnant gouging in the cost of hospital care, doctor's visits etc redounds mostly to the profit of private insurance who provide no social value in return. The exorbitant cost of medicine does indeed flow to pharmaceutical companies, but the particulars of how they would be affected depend on the details of how universal health care was implemented.
> complaints that our health care is 'too expensive' never seem to take into account that our (expensive) health care is the best in the world
I have no idea where you got that notion; the US is generally not ranked in the top 20.
https://www.who.int/healthinfo/paper30.pdf
https://healthcarechannel.co/how-australian-healthcare-ranks...