Government certainly has its hand in medical care. At the same time, there are “private” hospitals.
Does it make sense for me to walk through WalMart’s doors without the ability to pay?
There is no such thing. Hospitals, Doctors any health practitioner must have a Government license.
When I was young there were private hospitals, mostly charitable owned by churches. Little charity was handed out, you had money, or insurance, you got in, else you didn't. I was born at home as was my brother, doctor delivered, no idea what that cost, but my father was erring 50 cents a day at the time.