I have a bit of a problem with the all or nothing framing this discourse usually has. I think that libraries should make an effort to stock evergreen classics in addition to the recent, hot, and in demand. The new ones will be checked out a lot, then fall off, and then the library eventually gets a new batch of new hits.
They do serve a lot of people with this method, but am a different cohort. If a library is to serve a diverse group of people it should also remember book snobs like me. When I visit my local library it is as if anything remotely classic is hidden in a secret area, you can’t find hardly any of them.