This particular analogy is a pretty interesting one because right now, the government is hewing pretty closely to interfering with Americans' right to HC. While you may not believe the government is the best way to deliver healthcare (which is a fine opinion to have), I just read
an article about the litany of ways the Trump administration is working to undermine current healthcare law.
I think your premise is about the difference between inherent right & prohibitive cost. My point is it is a very fine line between the two & they may be intermingled in some cases.
For instance, if the only reason something is prohibitively expensive for someone is because of decisions by another party to make it so, one could reasonable argue the latter interfered with their right to have it. It's not that the government merely didn't PROVIDE something; it's that they actively work to AVOID their stated mission to provide something to citizens. Presumably because A) they hate why that dynamic exists B) they don't want to spends money on it & C) they disagree about whether it is a right in the first place.