We in Hungary have a "free" healthcare system, which is available to anyone. Anyone who have money avoid the system since its quality and handling of people is unacceptable. Still, you cannot just die due to uncovered healthcare. ...It'd just feel worse....
What I mean is "free healthcare" is just a question. First, healthcare have a cost which should be covered by someone, some way. Second, there is a question of what you get for the cost. Third there is the problem whether the quality of the free system is reaching (or above) the minimum required.