The "deeply held moral conviction" is that a nonproductive citizen's need constitutes a valid claim on a productive citizen's wealth. Far from being a moral conviction, the basis of that feeling is the ultimate expression of immorality.
I agree with you, though, that no amount of explanation is going to make the misedducated public understand just what an immoral concept they are embracing when they call for such free services.
Moral or immoral, it is reality. Human nature. I am a free market type guy. But if a family member needs a heart, I'm going to get it for them. And I think most would. Principle be damned.
As for myself, I don't care. Gave up years ago expecting I would have the same level of care my parents have had. But I don't know many other people who feel the same way.
Libertarians can create all the wonderful scenarios about how things should be but they are going nowhere unless they compromise and use some libertarian/free market concepts to improve a system which human nature demands we have.