proper public health system.
A couple quick points. HealthCare is a privilege of wealth, not a right. If you want to assert that is a privilege of citizenship, that is fine, but make sure it is clearly defined as such. FYI, Privileges can be revoked by social contract, rights exist apart from social contracts.
The problem is insurance, but not in the way that you think. Middlemen increase prices, every time. Every proceedure that is not covered by insurance, is always much more affordable, and much more available when compared to procedures that are performed primarily by the insured, and are improved at a much faster rate. Laser eye surgery used to be quite expensive, and wasn't covered by insurance. It quickly became much more affordable and had vast improvements as more and more people paid for it (out of pocket, not covered by insurance).
National or even State run health care sucks. I have relatives in France and while they love Nationalized Health Care, they hate going to the doctors / hospitals because of how bad they are.