I will say this: I've never asked for an arXiv endorsement before, but I have cold emailed professors before to inquire about certain aspects of their work. Not often mind you, but once or twice. And I've told this story here before at some point, but the response I got the first time around was overwhelmingly positive. I'm pretty sure the guy was thrilled that anybody was interested enough to read his book and send a question about it. He sent the data I was looking for, a pre-print of another related forthcoming paper from his group, and a standing invitation to reach out with additional queries in the future.
So based on that n=1 anecdote, I feel pretty good that at least some academic types would be happy to provide an arXiv endorsement to somebody doing work related to theirs. It's no guarantee of course, but my hunch is that if one is doing non-crank work, they can probably find an endorser with some effort.