They don't want a motivation letter to be written by an LLM (because it's specifically about the personal motivation of the human candidate) - as far as I can see this not reflect either positively or negatively on their level of optimism about AI impact in general.

Companies, especially large, are not interested in fads unless directly invested in them. The higher and steeper the initial wave the bigger disappointment, or at least unfulfilled expectations happen, not always but surprisingly often.

This is just experience and seniority in general, nothing particular about LLMs. For most businesses, I would behave the same.