Librarians who refuse to give up paper books are like record shops who refused to give up vinyl.
You write this as though the "physical vs. digital" battle has long been fought and won. The reality is that the landscape has barely begun to be fleshed out among libraries, and despite that, libraries are already adjusting their budgets to accommodate the inevitable sea change. The stereotype of the stubborn librarian in sensible shoes and tweed, clutching her Emily Bronte and refusing to acknowledge the existence of digital books, just doesn't represent the mainstream position among librarians.