At a very decentralized level, yes. Or at least some form of provision for any citizen, but I don't have anything against private health care as long as the goverment and the private sector don't entwine each other too much.
That's the problem with the system we have as it stands now. We have way way to much government paperwork involved in health insurance. It didn't go to hell until HMOs came about and prior to the 1980s this country had no problems handling a private healthcare industry, hell in the '70s into the early '80s doctors made house calls!