There should be a basic law of health care: no person is liable for a debt they incurred before they were presented with the price and had an opportunity to refuse. I'd give some amount of leeway for unconscious patients, but aside from that every single penny of expense should be agreed to up front. The absence of this policy explains a lot about how things have become so perversely broken.
It's an interesting question.
Health care is a human right. Therefore it must be free.
A prompt and fair trial is also a human right. Therefore legal help must be free.
Moving around, staying warm and basic hygiene - a lot of stuff sound like basic human rights, but very few argue that transportation, heating and sewer draining services should be free.
I think most people around don't mind paying for the service. They just want the prices to be reasonable and predictable.
Oh, you're preaching to the choir, but I'm not optimistic about our country's chances of doing the right thing. If we're not going to follow the successful examples we've been presented with (because it's socialism! /s), and we're going to have capitalism, then we should have capitalism and engage in transactions where both parties have complete knowledge.