Financially, what's the difference between paying taxes into a health care system that benefits everyone and paying premiums for an insurance policy you may potentially never end up making use of? Those premiums you pay to your insurance company are paying for the health care of other people.
What exactly is the difference, realistically? Because it seems to me that one of the biggest qualms is people don't want to be paying for someone else's care. Guess what? You are either way.