animals might be thinking
I liked it: the pigeons think, what for are you bothering us here

. But seriously, I think that people will not reach such a state that they poison pigeons like rats. Doves are the bird of the world.
Killing pigeons like rats is very possible especially when they are too many and become a pest already. Animals can be great to look at and even takes the stress away but some of them become invasive species when there's is no predators to maintain the population. If they become a menace already, it's not going to be good for the ecosystem.
But they are birds still. Though domesticated they are meant to fly free all the time.