Our libraries have mostly moved away from this model. I may have some details mixed up but I believe there was a study done that showed books were more likely to be returned without the late fee than with a fee.

Basically people will feel ashamed or embarrassed to return a book so late (or maybe in extreme cases cannot easily afford the couple dollars) so they end up stealing the book and never returning it. So now the library has to buy a $10 book because someone couldn’t pay the $5 late fee. It just makes more sense in the long run to let people bring the book back late without penalty vs not bring it back at all in fear of a fee.