Here in Ontario Canada we have OHIP, Ontario Health Insurance Plan. It works for the most part, covered by taxes we pay nothing for doctor or emergency visits. For the most part medical tests are covered, a few exceptions one of which I can't understand, women do not pay for mammograms but the gents pay for PSA tests for prostrate cancer.
Emergency rooms are crowded and patients are taken on a "emergency" basis. In otherwards a possible heart attack gets in quick, a drunk teen that got in a bar fight and sports a cut lip can wait.
It is a system prone to abuse when one lives in a border town. Windsor, Ontario for example is a mile away from Detroit, Michigan. Examples of phoney addresses abound, and a lot of the downtown bar fights result in treatment being given to Michigan teens who then skip without paying. Try to never need emergency treatment on a Saturday night, you could wait for 8 hours.
So our system works for the most part but like anything else it has it faults.