> Then compare USA and EU.

There is no EU-wide health system of any kind. The EU is much less integrated as the US, it's really not close to being the "United States of Europe", even though many are pushing towards that direction.

> And they figured this out by putting different authority on different levels.

As have the US, apparently. Each state does what its inhabitants want to do and pay for. The argument is that because European countries have federal systems, so should the US. If you now compare the US to the EU, then there is no federal level health care system in the EU, only at what would be the state level when compared in that way.

The EU directly regulates pharmaceuticals and medical devices. Via different measures (for instance by regulation over cross border treatment) it defines some common ground rules. True, it's not a single integrated system, but variance in EU is lower than the difference to US.

> True, it's not a single integrated system, but variance in EU is lower than the difference to US.

As in "there are public health care system in the EU", but that's not because of "the EU" but because of the nations making up the EU using similar approaches in that regard. It's not that we all had some random thing going and then the EU decided in 2004 that we should all do a public system when Eastern European countries joined.

Please don't change history here. There is no EU-level health care system, the EU has not created public health care systems in member states and European countries do have varying approaches to health care, with more and less concentration on state-run programs.

Yes, historic reasons are relevant. However it drives some alignment. Among other things for new members chapter 19 of the enlargement negotions covers different aspects. Thus in order to join some aspects have to be changed in different countries and U.S. won't be able to join (of course U.S. is failing the initial test if being an "European" country in first place)

And yes, there is quite some freedom, as British didn't want to replace the NHS, while Germany wants to keep their complex system, with private and public insurances and the assistance for state servants and all that ...

That's how the U.S. operates today. Schools are run by the state, although they do get some federal subsidies and those come with a lot of strings attached, they are largely run by the states individually. And in K-12 each school district has its own administration. The colleges and universities, except for the private ones, are run by the state.