I am Australian, and I am 72 and DW 67. We have private health insurance, which costs us about $3000 a year. The main advantage is that we can jump a queue at a public hospital, and the minor advantage is that the food in a private hospital is better than at a public.
We also do not insure for dental and optometry.
Recently I was diagnosed with early bladder cancer, now in remission, and when the specialist knew I had private insurance, I had an exploratory procedure a few weeks earlier than if I had to rely on the public hospital. Bills vary; my first cystoscopy (what is known as camera surgery, to see what is there) cost $200 for the anesthetist, and $80 for the specialist, these charges being above schedule fee. I was referred to another specialist which cost about $200. I have had a few more cystoscopies, which cost nothing. Schedule fee is what the health professional is paid from the national health scheme. Private insurance can cover part of any surcharge charged by the health professional. I understand that surcharges by health professionals vary a lot. They have to pay off their Porches somehow.
I am happy with the Australian system.
My local doctor (do Americans call a local doctor a GP, as we do?) charges more than the schedule fee, about $12 more, but his surgery is within walking distance.
A hundred years ago, a national health scheme would have been less effective, because doctors had less power to cure illness. The more effective doctors are, the more society had to pay to keep living longer.
Australia and NZ got a national health schemes mid seventies, and we thought we were slow, compared to Europe. Canada got a national health scheme about mid eighties.
Watch Michel Moore's film Sicko.