The U.K. and several members of its Commonwealth group have government health insurance or simply government health services. The basic goal is to provide needed health care to every citizen without reference to their ability to pay.
How does this work in practice? In every case, demand for health care exceeds the voters' willingness to be taxed sufficiently to pay for all that would be used.
How do governments cope with excess demand, for which they lack sufficient resources? Rationing - treating life-threatening problems immediately, treating non-life-threatening problems whenever time permits. Painful knees and hips get replaced after waits of a year, or two, or three. Backaches may never be treated.
During these waits, some die without being treated. Some spontaneously heal, some seek the comfort of street drugs. Too many suffer. Those with resources may utilize non-governmental health care providers.
Some nations, like Canada, are offering physician-assisted suicide as a realistic alternative to a life of unremitting pain and immobility. I find this option less objectionable than many do, although I can't approve of it.