The library card itself is mostly meant to make sure the people borrowing books are known for purposes of late fees etc. It's nothing else than an account registration, the only reason it sometimes costs money is because the library is meant to attract only a small specific area of a city (the others have their own libraries) but due to a lot of communter traffic they're worried about X-times the amount of estimated people getting books from this particular place.

So they make the cards cost a tiny amount (I think I paid €5 before) so that you won't just want to get a card from every single library in your city.