I haven't used it personally but I'm pretty sure the library with the garden that's near me actually uses the garden for classes to teach children about things like how insects pollinate plants and how to grow stuff. I think it's mostly an educational tool as opposed to a way to feed the neighborhood on the tax payers' dime.

Maybe community garden is the wrong term for it. I would also be a bit unhappy if my taxes were paying for a library to feed the neighborhood. There's other/better ways for the government to give food to people from collected taxes.