Medical care will always be limited in the real world, no matter the system. There's a bunch of possibilities:
Limiting what you can be treated for (EU)
Oh and this is horrible too. When the government is forced to implement limits such as this, they always carve out their own care as a special case (yes, Parlementarians and government officials have different, better, health care, especially when it comes to long-term care, coverage outside of your own country and emergencies. The UN has it's own system as well, for example), and they impose limits.
In Belgium there's a joke. There's 2 treatments in Belgium that are not like everything else when it comes to national health insurance: anorexia for teenagers and a certain congenital disease. They are covered despite it being a BIG negative in terms of money for the insurance/state. This is strange, it doesn't match what they "usually" do at all. Now one might go and check if what the daughter of the prime minister is in treatment for (she's a teenager). One might check what the daughter of 2 prime ministers back, French side, is in treatment for (she's much older, which is strange, given that given the particular congenital disease life expectation ... without gene treatment which is normally a no-no for the national insurance. Just look up "Baby Pia" to see how much they fight it normally). I resent identifying the patients involved to this degree, but obviously their family relation to currently in power politicians matters a whole lot in this case.
From everyone else "reasonableness" is required: for example moral limits. E.g. political decisions about organ replacement: no organ replacements allowed if you've been treated for drug addiction at any point in your life. No gene treatments, no matter how life-saving they will be. Strict (and quickly changing) limits to psychological care, as politically convenient at the time. Using changes in coverage to guarantee jobs. Etc.
Limiting how much is covered (US)
Basically you paid in X, you get Which do you want?
In practice, of course, to some extent both systems are limited in both ways. You cannot get treatment for absolutely anything in the US, and you cannot really exceed what you pay in for coverage in the EU (you can, however, in both system get insurance to cover you not working for a decade). But the emphasis of the different systems is very different. Mostly the above classification is true.
What was pretty popular when it was available was medical care, limited to cheaper care. Making sure you get expertise when dealing with a broken leg or pregnancy or ... but for example explicitly excluding psychiatric problems (which are really expensive). However, this means the government has to provide a place to live for people who cannot live by themselves and so the government always insists this is included in private insurance. The problem, of course, is that it's both necessary for some people and easy to abuse to get long-term care without a job. Since the government doesn't want to pay for this largely but not entirely abuse of the system, they force it into the insurance.