Our family doctor made house calls for urgent matters and for all I know he still does. But only after his consults are done of course and only for something urgent. The last time it happened for me, was around 1989 or so. I had been ill with some sort of pulmonary thing for a week but still kept my shop open despite it all. Then late in the afternoon I crawled into bed and was sort of out of it for hours, almost ready to die for all I cared then. My wife had to leave for her job at the hospital, so she called the family doctor and he came by after she had left, maybe around 22h. As luck would have it, a lady friend of ours, a nurse, dropped by and she stayed until the doctor came. They both knew each other and after giving me some kind of injection (gamma globulin I think) they all had a fun get together.
My parents both had their doctor come by for non urgent house calls up until several years ago, when they passed away. And in all honesty, the times I was there when the doctor came by, I felt like he was just going through the motions, getting it over as quickly as possible, since nothing was really urgent, just routine stuff like filling prescriptions. But they lived in a semi-rural, suburban area, a sort of escape-the-city-and-minorities enclave, and the inhabitants there were pampered - and fleeced no doubt - by businesses and tradesmen and services in the area. Expensive house calls for inconsequential things being part of it all.
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In Belgium, if individuals make use of the ER for non urgent matters, they have to pay a surcharge. I think it is 50 or 75 euros, which doesn't sound much to an American, but which is around 8 to 10 times the normal charge for a medical consult. So it helps to keep away the non urgent cases. But what constitutes urgent? If you are admitted to a hospital room then your case was obviously urgent. So are broken bones.
But it's a bit arbitrary I think. Once my wife got caught between 2 fighting cats at night and her lower leg was cut open for some 15 centimeters, a real nasty gash pouring blood. She obviously needed stitching so I took her to an ER where she was sewed up. But, since she wasn't admitted, we did receive a surcharge afterwards, which I thought a bit excessive. It doesn't seem right to have to wait some 12 hours for normal business hours to get an open wound treated and sown up. A wound requiring stitches is somewhat similar in urgency compared to a broken bone.
But whatever, the surcharge was worth it.