Why? You're conflating a hyper authoritarian scheduling system with a vastly superior simple and cheap billing system.

There is no particular reason both have to be implemented at the same time. Maybe its culturally popular but there's certainly no technical reason.

I live in a former 1st world non-socialized medicine country and I have no option in where I go for medical care other than on a very meta level of which employer I work at and where I live ... in an emergency (heart attack, car accident) the ambulance drives me to the closest ER, there is no free market deciding which is "better". In a non-emergency, my cheap health insurance contracts with precisely one large medical chain in my area, so if I'm willing to do something like medical tourism and fly to another state I could select a new doc, but again no free market ...