In the case of tennis lessons, you could refuse the service and simply go home. You would simply miss a tennis lesson. Or, you could setup a Venmo or PayPal account AFTER you receive the "service". It only takes a few minutes and doesn't cost anything extra and would allow you to pay the AGREED UPON rate without a problem

On the other hand, at an ER you can't choose your doctor most of time, especially at smaller hospitals. And most likely you've gone there with a problem that needs immediate attention so you don't have the choice of simply going home. You're thinking that you have gone to a hospital that accepts your insurance and your insurance's agreed upon rates (in network) and you probably don't even realize the ER doc does not until the doctor's bill comes. Like Venmo and PayPal, you can't sign up for the doctor's insurance afterwards and are now faced with an additional, higher, surprise fee. Thus, you are forced to pay more than you thought and you need to pay it out of pocket (or argue until the doc gives up).

I understand the plight of docs having worked in health care and having docs in my family. I understand that much of this is caused by our current private health insurance system. But, as you said, you do need to consider both sides.