There's no way card fees or late fees could ever fund a library. I'm pretty sure those are just policies enacted by people who either don't understand or don't care.
The late fees are usually miniscule and they act as a deterrent to keep people from holding onto the same book for an extended period with zero repercussions.
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.
And I don't know how stuff works in America, but where I live with most public offers like libraries, public pools, graveyards and stuff like that the amount that the user has to pay is almost never enough to completely fund that thing.
It is still good to demand a certain price, since that increases the appreciation of this public good, decreases wasteful or careless usage and obviously helps to lessen the necessary subsidies from taxpayer money.
I am pretty sure the people enacting those policies understand that perfectly well.
If you would demand so much money from library users to fund the whole library, then noone would use it and a valuable public good would be lost.
I’ve also never paid for a library card and I live in the US, so it’s clearly not always America. In fact most commenters here are noting they are paying small fees in euros so it seems this trend is common in Europe more so.
Where I live, it's free for school children and people on welfare etc. For university students it's 5€ a year, for adults it's 10€.
So really not a lot, but you also get access to a lot of other online services for free (encyclopedia, streaming service for older and arthouse films, magazines etc.)
Late fees are just there to keep you from keeping a book or whatever for long periods of time, because then other wouldn't be able to read them.
when i was a kid, we lived on the 'wrong' side of a county line, and thus, in a different township than was part of the nearest (7 miles away) public library's "service area"... tax sources, jurisdictions, and all that jazz. it was outrageously expensive to get an 'out of area' library card.. at least that's what i was told. we never had one.
so our library was a tiny rural library that was housed in an old one-room school house. it was open only a few hours a day, a couple days a week; instead of the 7 days a week at the public library in town (an original carnegie library).
Back in the day, the library was much much more essential. It was the only access to advanced knowledge. I remember driving (riding) long distances to get to a better library for school projects when I was a kid. It was like the required Odyssey one did just to find an address to an outdated article that half mentioned what you needed but had no citations. It is hard to believe how isolated information was back 30 years ago. Big libraries were like a religious holy site of opportunity back then, choir, clouds parting, golden rays, Morgan Freeman, and all.
A significantly larger chunk of my taxes are being used to subsidize military killing machines for wars outside my country. I got complaints, but a library ain't one.