Yes. I agree that Gödel himself did not pay any attention to the implications of his theory in other areas.
But many, especially philosophers, have discussed the implications of Gödel’s two theorems in other areas, especially for the mind.
- For example, the last reference in the post, “Gödel, Escher, Bach – An Eternal Golden Braid”, by Douglas R. Hofstadter (1979), has been the topic of discussion among philosophers for many years now.