My sister runs a "Little Library" and her solution has been to throw money at it --- uninteresting/objectionable books are removed and books which she wants to distribute (often copies of books we remember fondly from childhood) are placed there.

I built a little free library a couple years ago. There are definitely people who drop their old crappy books. A good little free librarian treats it like a garden, pruning the weeds and letting the good stuff grow. I also like to seed it occasionally with some of my old favorites that I want someone else to enjoy. It tends to sort of perpetuate itself. People put less junk in there if there is already quality stuff.

The vast majority of books are crap.

The little libraries have a cross-section of crap (verified by comparing what you find there with Goodwill / other sources).

If you want a good one you'd have to set up your own and aggressively curate it.

I feel something like 90% of all books purchased each year are bibles, cookbooks, or self-help.

If you see a library that's full, find the worst book, walk a ways, and throw it away.

My mom was cleaning the house and gave me a tote filled with books I had left at home when I moved out. So I drove around and stuffed all my Goosebumps and Animorphs books into all the little libraries I knew about in my area. I hope some kids had as much fun reading them as I did when I was their age.

If people own a book they probably liked it at some point.

Free membership which accumulates points. These can be spent on books. Books are priced in points according to a metric (TBD). Bad books are 0 points. You can also get points by bringing in good books.

(It's like uh some kind of currency based barter dude ;) )