This and many other new problems are solved by applying reputation systems (like those banks use for your credit rating, or employers share with each other) in yet another direction. “This customer is an asshole, allocate less time for their requests and warn them that they have a bad history of demanding nonexistent books”. Easy.

Then they’ll talk with their friends how libraries are all possessed by a conspiracy, similarly to how similarly intelligent people talk about Jewish plot to take over the world, flat earth and such.