A library which was known for having a "last policy" system in place, should not have this difficulty. I would further argue that any library should be willing to accept a copy of any book which they do not have and safely store it until someone wishes to borrow it. I'm still salty that I had to buy a copy of Glenn Reid's _Thinking in PostScript_ when a local library discarded it from their stacks (there are other books which I would check out semi-regularly which have also been discarded which I also need to purchase, but missed seeing on their "discarded" table or at the annual library sale).
Yes, this would require better funding, and yes, I regularly donate to my local library every year.
Yes, but the principle here is that a library (system) should function as a repository for physical embodiments of knowledge, and should not be discarding books.
We're going through this at my workplace as well, converting from cubicles to an open floor plan, so workspaces which had decades of accumulated books are being cleared out --- I've rescued as many as I can justify from the recycling bin, but that's a tiny portion, so I'm feeling this sort of decision quite viscerally.
I think the library system does a good job of that. For example, here's the WorldCat entry for Thinking in PostScript[1] that shows its 4 editions physically available at 107 libraries. It's also available as an eBook and (since 2024) on Archive.org[2]
Which highlights why Archive.org is so important as an archival and lending library. It's like the idealized version of microfiche. The content of the books have been made so small that not only can they be trivially stored, but beamed to your pocket at any time, almost anywhere in the world.
There are at least ~158 Million books in existence as of 2023[3], and between 2 and 4 million added every year. To ask that each library be an unopinionated store of physical books is too much, and reduces their function to a well-organized warehouse, when the real power of libraries are its librarians. They are research specialists available to anyone and everyone, and well worth a conversation the next time you want to know just about anything.
Yes, this would require better funding, and yes, I regularly donate to my local library every year.