A lot of the bad actors are scanning prices on them and selling them. Deface the title page and inside covers and they will be fine to read but worth almost nothing at sale. A stamp saying "Taken from the Little Free Library of X. Share and enjoy. Please report sellers." would do the job.
Where I live actually has the opposite; there are ~6 within a mile, and they're usually completely full. People are always dumping huge collections into them, to where I never even have the chance to give back myself.
I don't know what makes it different here. But it is possible for them to work without safeguards.
People frequently take all the good books, all at once, and don't return them.
Someone just emptied out half of it yesterday, and I don't even think they were picky. They just took a whole shelf of books.
It's such a crappy thing to do, and there's nothing that can be done to stop the bad actors.