Late fees do have one benefit – what if someone has a strong interest in one particular book (or a handful of books, which fits within their borrowing limit). Maybe it is a textbook or reference book for a course they are doing. Maybe they are just an obsessive person. They want to borrow a book for far longer than the standard borrowing term, or even indefinitely. They don't care if doing so blocks them from borrowing any further books, because they are more interested in the book(s) they have currently borrowed than in any of those.
Before, if they didn't return it, they would start getting late fees. Some people may be so intent on possessing that book, they may consider the late fees worth it – viewing it as a rental fee rather than a fine. But others, the late fee may be enough to convince them to return it, whereas merely suspending their borrowing privileges would not.
And this can make a difference to other library users. Ever wanted to read a book, or even borrow it, but you can't because it is out on loan? Abolishing late fees runs the risk of making that negative experience much more common than it was before.