A friend and I analyzed doctors thus:
There are two functions of a doctor:
Expert Mechanic. Uses superior domain knowledge to actually repair damage to your body, prevent infection and sickness, and give you necessary expert advice.
Voodoo Priest. Makes you feel like something is being done about your ailments. This is doubly important because the placebo effect is real: making you feel like something is being done can often be enough to make you better, besides calming your anxiety.
The problem with modern medicine is that we don't believe in the second type of medicine, even though it's real and important. So even for the voodoo psychosomatic aspect, we have to come up with "scientific" medicine to make ourselves believe that we are doing something. This drives demand for ever more expensive "rational" procedures, and the system ties itself in knots and consumes a lot of resources to deal with the inherent contradiction in finding scientific-rational solutions to psychosomatic-spiritual problems.
For example, imagine you have a pain in your leg. You go to the mechanic-doctor, he says, "I dunno, just make sure you're sleeping, eating, and exercising right", which may be legitimately all that rational medicine can do for you. You are not satisfied. Consider these two alternatives:
You get mad and push him to give you something. He prescribes expensive antibiotics or pain-killers, just to be sure. Both of which have some side-effects and externalities. You've settled your mind, but wasted a bunch of resources to do so, and possibly contributed to the creation of a superbug, or taken a risk of a bad reaction.
You say "well fine, if you can't heal me, God will". You go to the priest, and he prays for you and does some nice ritual. You feel the light of God pouring into your leg, and it feels better. You have settled your mind and probably helped whatever it was by the placebo effect. Maybe that's all there was to it, but maybe it just tides you over until the real problem gets bad enough for the mechanic-doctor to actually diagnose and fix. Either way, this is cheaper and safer than what we do now.
So for rational-worldview modern people, loss of actual belief in magical or faith medicine might constitute a loss of valuable social technology. I don't know that there are any important immediate implications of this, but I'm now much softer on safe and cheap pseudoscientific "alternative" medicine.