Technically the real reason you shouldn't feed animals is because they get used to getting the food easier than usually in nature and when you stop giving it to them they waste too much energy searching for new sources. its better to leave the birds to find their own ways to survive rather than relying on people to feed them. They aren't your house pets, you wont be there every day to feed them. But the Mutated Pigeon concept is a nice twist.
That's how we keep them in check and prevent the bird uprising. We even took the time to domesticate cats in case it failed.