Yes, yes, maybe (see OP’s blog post).

To my knowledge, none of the negative sentiment regarding AI has ever been directed at its medical applications. Maybe the AI companies should instead focus on those things.

OK,

I should have put have put things as "when you are primarily interested in some benefit outside of the task at hand". Some of those benefits might be great, sure. But it's still not necessarily going to improve the enjoyment of the professional.

Edit: Also, not all of the things on your list are the same. I would note that P!=NP would be a theorem whose proof would offer no practical benefits except for the potential mathematical machinery created to achieve the proof rather than what it tells us about practical algorithm time (the theory is about worst case, not average case, an algorithm that's O(n^100) is as effectively intractable as an algorithm that's O(2^n), etc).