(EDIT: I had not read thoroughly your comment, see my PS below for a direct reply.)

Your point is to use a proxy for the variable that really matters.

Unfortunately that proxy is neither reliable, nor has good impact on the society in general.

It is better to just use the pertinent variables directly without a proxy.

Your physician is good if e.g. they have also a research formation, if their patients are satisfied and have a good recovering rate for illnesses that promise recovery, etc.

PS: ok, I see that you also point to variable trust from the patient to the physician based on superficial criteria. I hope that can change in the near future when everybody has the mindset "the appearance is not what matters". The patients themselves will benefit from growing their openmindedness.