Restricted supply of physicians means that there aren't enough of them to open a competing hospital.

Your complaint against for-profit hospitals would apply just as quickly to a nonprofit hospital in a socialist regime. The fundamental problem is monopoly. Because most people don't behave nicely unless they are forced to by market pressures. Whether those markets are economic or social in nature.

Even if you ignore present-day socialist economies, you can look to NIMBYism in the developed world as a flagrant example of what happens when "normal people" gain collective control over a resource without any competitors. They immediately weaponize it to the harm of greater society. If not for financial purposes, then ideological ones.