We actually considered a pigeon trap and relocate business in LA, CA. Funny thing is, they didn't want them harmed, just relocated. Job security.......
I have been getting paid recently to harmlessly relocate some pigeons to the landfill...by a nameless agency who will deny all complicity.
I'll bet you guys don't know that pigeons breed all winter? Not only do they lay eggs in winter, they are excellent parents. They continue to feed the chicks until they are quite large. We caught several of them, and couldn't figure out why they didn't fly away.
I even took a pair home, and they were quite happy sleeping in an open box on the back porch. I couldn't tell them from fully adult pigeons from their size, but they certainly acted stupid. I took a bunch of pictures with the wild birds perching on my hand, outside with nothing keeping them trapped. They were perfectly content to keep loafing around, just waiting for the next free meal.
My dog took care of that attitude. One dead, the other took to flight and never came back. My wife was delighted, my daughters...not so much.