In my country (also EU) the public health system is most definitely not "free". It is paid for by a universal tax called (insidiously and inaccurately) "health insurance".

> There's lately though talk about unvaccinated COVID patients bearing the cost nonetheless.

Calls for true insurance (individualized, based on actual health and habits) are completely infeasible for political reasons.

What I can see happening is the existing mandatory health tax PLUS extra payments for non-grata groups. Some constitutional changes may be needed, but since all the right people would profit (extra $$$), that's just a technical detail in this day and age.