[tokenadult]

I've met quite a few doctors and my impression is that their average IQ does not compare very favorably with that of coders or engineers.

You have undoubtedly met fewer doctors and fewer coders and engineers than I have. (I'm older than most people on HN.) Anyway, IQ is not the relevant issue. The issue is specific training and clinical experience. For equal IQ scores, I will ask engineers to solve my engineering problems, and doctors to diagnose and treat my diseases. If each professional has passed the required training course and has continued in practice with a license with good reputation, I don't need to ask IQ scores before I seek a doctor or seek a coder. What's important is getting the work done right, and doctors have better background for doing medical work than engineers or coders.