I disagree with your analysis. I think you are wrong.

Health Care is a natural monopoly like an electrical system. Basically, a large portion of health care the creation of infrastructure that everyone benefits from. An MRI machine or whatever is benefit to everyone since everyone might need it even if only some people actually use it, etc.

For that reason, the cost of procedures, infrastructure, etc, etc. are infinitely debatable and there is no true way to way to assign costs. And sure, the actual assignments are irrational but framing this "things are subsidized" has things exactly backwards.

Here's scenario - suppose electrical companies weren't responsible for maintaining their own grids and homeowners had to individually maintain insurance in the event of a pylon going down. Suppose if you didn't have insurance and could be tagged as the last user of a substation, you could in-hoc for the entire cost of repairing a pylon or whatever. This would only approach the irrationality of private medicine but I think it illustrates the situation. (and the finance system might manage to put that in place too if we're not careful).