That is dumb as hell. It's not "unethical", other applicants can do the same and if they don't, they will actually have better chances because they will stand out from the crowd using AI to write it.

We all copy from others, ask help from friends and family or from professionals, we need to stop pretending that we don't and that we are "original". I wrote my first cover letter 15 years ago by googling an example on the internet and changing it a little because I had no idea what to put in it and I have never seen one before.

Same crap with the artist and AI generated art drama. Every single artist in the face of the planet learned by coping what countless others do and did, exactly the same as AI.