For true "public health systems" you need to go to the USSR or Cuba. Where all doctors are state employees, all clinics with their equipment are state property.
We still, fortunately, have private medical care system.
It is a VERY reasonable assumption, what removing that private element from the health care would cause it to collapse to the above mentioned examples.
Constantly, I read some British articles: "WOW! A new, breakthrough cancer treatment is now available in the UK!!!!"
Cool... we had that treatment here 18 years ago. And the British system is not even a true public one.
