Financializers and engineers so often miss the human factor, or try to design around it. At some point in this process involving care for humans, you have to rely on people simply choosing to do the right thing, even if it's hard. This has been medicine's tradition for a long time. The fewer layers between doctor and patient the easier it is to do this. You also have to provide enough resources for them and some kind of work/life/pay balance.

In Canada we have fee for service, with incentives to care for specific populations (remote or chronic conditions etc.) Doctors (or their clerk) do their own billing direct to provincial health services. It works. We rely on individual morality and they generally do the right thing. Our outcomes are good.