Your entire argument works just as well for shamans as psychiatry; except the drugs shamans use have far fewer and more benign side-effects, with thousands of years of history instead of 20-40.

Many of the psychiatrists I have encountered "believe" in their medications, and when questioned as to how (and how well) the drugs they were informed about work have no real substantive argument for all their years of med school.

But fuck, do they get paid better. You won't see many shamans on a Pfizer sponsored golf trip in Hawaii.