Just look at public education as an analogy:
Everyone is forced to pay for it (through taxes), even if they don't use it. Only the rich (who have after-tax money to pay for private school) can avoid it. And they do.
The politicians who enact the system almost universally avoid the public option.
It's hugely inefficient; we spend more and more per student with diminishing results.
Over time (decades, mind you) we have come to accept mediocrity as the norm. It's a slow process. Nobody notices. Most don't know any better.
Innovative improvement is squashed through lobbying from the entrenched public employees (who benefit from the system), and through the absence of any vibrant "private" element. No one knows how good it "could have been" (if there was real competition/innovation in a private sector), so no one knows what they're missing. Being "no worse than last year" becomes a good thing.
Over time, the profession draws weaker and weaker college students to enter the field.
Add rationing (and don't kid yourself, there MUST eventually be rationing in some manner), and you have the future of American medical care.