"If I think everything should be fair and that I should be able to access care with the money I've already put into taxes, why can't we just convert everyone to health savings accounts?"
This common-sense question was asked by a close friend (and conservative). Firstly, compassion. Humans, especially Americans, recognize that there are times when you're not feeling well or not doing well that allow you to be excused from normal expectations.
For instance, the idea of a "sick day" is a social understanding by society and business that you have been given a brief reprieve from your work duties for a set amount of time. Extrapolated to a larger platform, you have the whole "disability" network wherein people can be compensated for a perceived loss of ability and financial hardship.
For individuals like this (along with children, the chronically ill, and elderly patients), they would be unable to have their own health savings accounts and, subsequently, would require help from the system.
Unfortunately, health care doesn't currently provide readily accessible prevention strategies and does not readily reimburse or promote supportive strategies, such as social workers, case managers, counselors. Many people who would fall into this category then cost the current system more than if we had a P.S.Y.C.H. system.
Secondly, there is power from shared social and fiscal responsibility that drives the "fairness" narrative to which Americans are highly alert. For "everyone to pay their fair share" won't be possible (which is why we have a progressive income tax, sorta). But having everyone pay something helps paying taxes and fees feel easier.
Thirdly, we love transparency. Having a general health fund that you can see and monitor is more transparent than individual health savings accounts and may help with decreasing that feeling of "us versus them," since we're all in a pot together. However, that's not to say you can't have your own individual health policy (which you totally and maybe should have).