The reason I used the library analogy is that at least where I live, library's are only run by the state.

And literally the whole point of this conversation is that Facebook has a monopoly on locally targeted online marketing, they're not stopping you from advertising on Myspace, what's stopping you from advertising on Myspace is that it's pointless.

Sure, technically Facebook doesn't have a 100% perfect, totally clean monopoly with literally no competitors, but that doesn't mean that them owning a significant majority of the targeted local advertising market isn't a monopoly problem and shouldn't therefor be legislated against.