There's a whole class of people who practically live in libraries, which makes your example very realistic.
It's one of the few places I know of that has plenty for young children to do, is open in all weather, is anywhere close to home, and doesn't cost an arm and a leg to get into.
I could also imagine someone working remotely having high library utilization.
Most co-working spaces charge $20-$100 per day for a desk.
And of course, plenty of people use them as a place to read books, magazines, and newspapers.