Earlier quoted context omitted.
An ADA compliant bathroom is almost 200sqft. And they will need at least 2 of them. So now that 1000sqft is now 600sqft. And they still need a place to store and process books, reading rooms, etc.
Also there's a big difference between a general "children's room" and strictly enforced "adults only" and "for children" section, with risk of costly lawsuits if some extremist parent thinks the kid saw something "obscene". My library had a children's section and even some toys, but I could walk in and go anywhere. Since I'm not American I don't have a good idea of what 1024 sq feet is: it's about 95m². I laughed out…
Ignoring that, they don't even need a room. They just can't let kids access it. A locked armoire near the checkout ought to suffice.