I think many regular people would be turned around in this issue if they got to experience the other side.

E.g. a regular American person could experience being able to walk into the hospital, giving no information other than their name and age and get treated -- then leaving with the peace of mind that there'd be be absolutely no paperwork, bills or insurance hassle to worry about.

Also - staying in a very nice private hospital with gourmet food, a nicely decorated room and great food might get some public health supporters interested in the private option (if they could afford it). I have the impression that American doctors would be less likely to say "Mrs X, there is absolutely nothing wrong with you, just go home and rest..." This attitude in public health can be a problem because doctors do not want to refer to specialists unnecessarily. Occassionally there are scandals where somebody was told they were fine but in fact they had a serious condition and should have been referred to a specialist.