Why is it nearly impossible for an organization to censor or destroy such a network? How is using fake birds such a big difference from using stationary access points?
You'd have to seek out and destroy nearly every node to disable it, otherwise it could just route around any damage or sabotage. And destroying so many flying things that are difficult to distinguish from birds would be no easy task.
Who would pay? Individuals. Buy a node, let it fly often, charge it otherwise, help create an open, uncensored communication network (such things are hardly unprecedented).
Who is going to pay to build such a thing?