IIRC the biggest barrier, by far, to algorithmizing the doctor-priest class's intuitional method of analyzing CAT scans, diagnosing, etc. was impediments by doctors themselves and their organizations, not the inherent difficulty of identifying the algorithm.

I think there are many cases where it's not just a failure to introspect that makes it difficult for people to explain insights or skills that come from experience. Introspection just doesn't work very well in such cases.

I accept that one might not be able to convey the experiences that lead to the insight, but one should be able to state the insight ex cathedra so that relevant counterarguments (those not dependent on having gone through the exerience) can be identified.

A characteristic example from the general population might be, "Hey, until you've actually lived through a plane crash like I have, you'll never understand why I'm so skeptical about aviation safety protocols." Well, no. Such an experience might give me a fear of flying, but that fear would be irrational. The fact that someone can't directly impress that terror upon you does not substantiate their conclusion, and so the experience differential is irrelevant.