There's another intuition that at least libertarians have, which is that it is not as bad to have undesirable things result from an impersonal process than from an active decision. It is bad if someone's house burns down and they couldn't afford insurance. It's worse if someone's house burns down, and they were in the class of people deemed unworthy by a bureaucrat of having their house rebuilt.
I think almost all progressives have the opposite intuition. They think it's better to try to produce an optimal result, even if that results in individual injustices (which it will--government rules are very broad brush, and will always involve error at the margins). I'm not sure how to bridge that intuitive gap.
It strikes me this is indeed one of the determining differences between those skeptical of and those confident in the ability of a centralized beaurocracy to actually improve the administration of health care (as opposed to its availability, which obviously could be improved simply by throwing enough money around.)
Given the range of viewpoints found around here, I'm curious what others think of this. Is this indeed one of the major dividing lines between progressive and libertarian/conservative viewpoints?