PS: Maybe the real way to fix this is paying a deposit upfront when becoming a member of the library, which is not high price, just the cost of an average book. You'd get this deposit when you decide to stop being a member.
How could that reframing work? Instead of free limited time lending plus optional fine after n days, make it a rental, but with the first n days free. If you return on time that's fine, but you're a freeloader then. Those who take their time with the books are the true supporters. Nobody will perpetually postpone returning because they feel uneasy about admitting wrongdoing (no matter how small).
[0] I believe it's only short term because bad habits usually take time to develop. Long term, the negatives will outweigh the positives. The person who would systematically take advantage of zero fine doesn't use the library, yet.
Now people will cancel their membership when they need their $15 back in fast cash. Probably the people who could use the library the most.
Do you have any idea how many people this would stop from using library services?