I've thought about something similar before in the context of explainable machine learning [0]. The author alludes to it - explicit knowledge is like an expert system. And I would argue that tacit knowledge is closer to a modern neural network that has learned from lots of examples. Asking such a system for an "explanation" - just like trying to encode knowledge in an expert system, inevitable doesn't give a satisfying result because of all the judgment and caveats involved in real live. A better approach is to judge competence based on past experience.
As an additional corollary, the tacit knowledge concept is a good argument against decision frameworks generally, which destroy information by trying to capture experience in a rubric.
[0] Getting more out of experts by focusing on results and not process: observations of people and neural networks http://marble.onl/managing_ml.html