> It is simply impossible to deliver unlimited, high-quality care to everyone.
Anything "unlimited" is impossible in a constrained physical world. So I am not sure what contribution you like to make by stating the obvious here.
For most economies delivering reasonable high quality care to everyone who needs it is totally a thing they can (and in some cases: do) afford. It is just a matter of priorities. You would be surprising what nations can sustain if they really want it. War is a good example. When a nation goes into a long war and changes its economy to support that war we call that a war-economy. It is an economy, that priorizes a lot of what it produces and outputs for the war effort. Nations can be years or even decades in war-economy mode without going under and that works because they priorize the nations existence (and thus the war) above other financial goals. And in war nations also make companies do things that would be otherwise unthinkable, e.g. make a company share blueprints with a competitor, favour certain industries with resources, etc. If any nation knows that, it would be the UK.
So if any modern western government goes all cheap and naive big eyes on health care, it is not because they can't do better, but because they don't want to. Not wanting to do better is a very easy opinion to have, especially if one earns money by being of that opinion. Those who suffer and die are also a different demographic than them, so even easier to pretend all is going well.
I am not saying that any health care system should be inefficient. It should be efficient in certain way (e.g. prevent funneling government money into pockets, prevent paying too much for medicine and equipment and so on). But efficieny is not the primary goal here, the primary goal is to have an adequate health care system. And you will always get unethical rich people saying private payer is adequate, because THEY are covered by it. But the fact of the matter is that everybody profits when a nation has a good working health care system for all, even the rich egomaniacs. After all they cannot decide where they will have a medical emergency as well.