Number theory might have progressed faster... we might better understand the “Great Filter”

Isn’t this kind of thing archetypal of knowledge that in no way contributes to human welfare?

In many historical cases, book burning has been a precursor to killing people.

Perhaps, but note that this wasn’t a precursor to killing people; people were being widely killed regardless. But the modern attention is not on the rape, murder, pillage, etc... it’s on the book-burning. Why the distorted values?

a high status of academics is arguably quite a good thing from a consequentialist perspective

Alvin Roth is no doubt a bright guy, but the idea that he has done more lasting good for humanity than, say, Sam Walton, is absurd. You’re right that Bill Gates has made a huge impact – but his lasting good was achieved by selling computer software, not through the mostly foolish experimentation done by his foundation. Sure, some academics have done some good (although you wildly overstate it) but you have to consider the opportunity cost. The high status of academics causes us to get more academic research than otherwise, but it also encourages our best and brightest to waste their lives in the study of arcana. Can anyone seriously doubt that, on the margin, we are oversupplied with academics, and undersupplied with entrepreneurs and businessmen generally?