Well, you made the case that police were previously privatized. I'm not sure that's true exactly. You also compare healthcare to police and fire services. I was just elaborating as to why that comparison may not be apt. Public health, insofar as controlling the spread of communicable disease, has always been a function requiring government authority.
The idea that people who set bones and cure cancer should be included in this category is a more modern take, one that requires much more careful discussion of what should and should not be a "public service".
> people feeling entitled to a service they previously resented as soon as it's useful to them
I think we should expect people to prefer suffering and death with dignity, rather than greedily and desperately peering into the pockets of strangers, but that's just my take.