The case for public libraries usually gets argued on the collection — free access to books, information equity, and so on, all true and all somewhat beside a point that I think matters more day to day, which is that a library is, before it’s anything else, a piece of civic furniture: a place you’re allowed to sit in for hours without buying anything, with a bathroom, with quiet, that isn’t your home and isn’t a shop.
There are very few other rooms like that left in most towns. Cafés want you to keep ordering. Malls want you shopping or leaving. Parks don’t have a roof or an outlet. The library’s collection is real and important, but I’d guess most of the actual hours logged inside a branch library on a given weekday are logged by people not actively reading a library book — students, people between appointments, people who just need four warm hours somewhere that isn’t asking anything of them.
This is closer to what I think we lose first when a library closes, before we lose the collection: not primarily the books, most of which exist somewhere else too, but the specific civic offer of an unmonetized room. Nowhere else in most people’s week works quite like that room does.