There are hospitals in rural areas here in the U.S., too.
Even if there is no hospital in a particular rural area, it would be possible for the state or local or even federal government to enact a plan so that a hospital is built there. That can be done without the entire medical system being placed under government control.
You’ve been polite with your questions. I hope you understand now why we object to socialized medicine.
Our system isn’t perfect. It needs improvement. (Less government might improve it, imho.) But it’s not the terrible system the universal healthcare-proponents claim it is.