There are still libraries that haven't computerized their catalog yet? I'm not sure I believe that.
(To be clear, I'm saying kids won't get the experience of specifically flipping through paper cards to find books, not the experience of using the library in general.)
I remember my family having an outdated encyclopedia because my aunt, a librarian, would hand off the old copy the library was trying to get rid of. I don't think I looked at them more than a few times, and even then it was only vaguely useful. Good riddance, online reference material is so much better.