Emunas Chachamin IMO does not mean i would trust a Gadol to perform brain surgery on me.
That’s straw man argument, because a gadol who is unqualified would not perform brain surgery. In fact, I have never heard of a gadol who performed brain surgery (although the Chazon Ish famously mapped out a plan for surgery which a skilled, practiced surgeon carried out successfully).
Part of emunas chachomim is trusting them that they won’t overestimate their abilities.