Doesn’t a protection racket beat you up / destroy your house / damage you in some way if you fail to pay?
Insurance (either private or public) doesn’t do anything negative to you if you don’t pay, you just don’t get any positive benefits.
It turns out that calling something a different name is a good idea when it’s literally a different thing.
I kept meaning to put aside some time and answer you properly, but I still haven’t. Your comment was well-written and it seems like you put some thought into it, so thank you for that and sorry I didn’t get back to you