And, you know, it can cut both ways! The story you are telling is one example. The town loses a lot of important library services, and everybody suffers.
Another thing that happens is unintended consequences. For example, Bill O'Reilly (a very conservative figure who supports book bans) just found one of his own books banned in Florida.
I don't know why it was bad, but he's pretty upset about it.
The thing is, for people who put these book-banning laws in place, there's no guarantee they'll be used the way the originators intended.
That's not exactly cutting off one's nose despite one's face. But I guess it's close!