Those wild birds bring everything into the yard - bacterial germs, lice, mites, worms, etc. That's the whole reason we have to spend so much money on preventive poultry care products against mites/lice/worms and spend money on vet bills for the bacterial/viral infections. There's no way to keep the wild birds away no matter how we insulate our chickens. Pigeons might be a little easier to dispose of as they are nothing more than germy flying rats. Cities around us have active pigeon irradication programs. Cutting down on the pigeons also cuts down on the frequent aerial predator problems as well. We don't have pigeons but wild Mourning Doves. There's no way to keep the Mourning Doves out of our yard as they swoop down to go after our chicken scratch mix. It's a losing battle unless you stand outside to shoo them off but they come back right away. Our Ameraucana used to chase the stray cats and doves off and finally gave up on the wild birds. You often see them all foraging together with the chickens.