gulp I did indeed mix up a confusing brew. Most of what I described was about Social Security. Medicare is a different, but related, component of what I was talking about.
Let's see if I can get it right this time: I draw Social Security each month, and I enrolled when I was 62. I could have waited until I was 65 years old but opted for the earlier date. Everyone who has worked - and paid into Social Security at any time- will eventually be eligible to draw. What I said about opting for the greater amount viz a viz spouses refers to Social Security.
When I become ill or if I need surgery, I present Medicare as my medical payer. It covers about 80% of a given cost. I have the option of enrolling in other insurance on top of Medicare if I wish.
Incidentally I was not intimating that the US system of Social Security/Medicare is the ultimate. Far from it. I am merely pointing out that Social Security/Medicare as a single payer does work.