Would you be ok with a system like Germany where you could opt-out?
"If I take death into my life, acknowledge it, and face it squarely, I will free myself from the anxiety of death and the pettiness of life - and only then will I be free to become myself." ~ Martin Heidegger
I've spent a lot of the last 19 years in Costa Rica and they have both a private system and public. I've been in both.
The public system treats the people like animals, eight to a room in the hospital I was in, with obviously poorly trained staff. I was able to get out of there and cross the street to a private clinic and everything was first class. Because I was not insured the rates for both were the same which was roughly $100 per day at that time. In the private hospital I had a large room to myself, a bed for overnight guests, a big screen TV, two nurses on call and doctors who were very professional. There was simply no comparison.
I save money by not paying insurance for my employees because it is just too expensive for what you get, so i pay for the private healthcare instead whenever they need it, including the birth of my housekeepers son. They are treated first class. I have too much respect to put them in public care facilities.