Carrying them by the feet I think is a more historical method, when you went to market with a basket on foot, it's not like you're going carry an empty cage too. You filled your basket and the stew hens got carried home by the feet. If you were taking 6 hens to market, they went by their feet. If you're loading a cage full and need to be fast, you grab by the feet and move the bird. Not taking a lot of time to fold the wings down and baby talk to it, when you have 500 of them to move. Head first into a butchering cone... held by the feet.
But for small flocks, pet birds, spoiled hens... no sense in traumatizing them. If you pick up every chicken you have that way, they're not going to come running to you for that to happen. They'll huddle in the corner and flip the heck out when you go to grab one. If you want tame chickens, you carry them around nicely.
I'll grab a mean rooster's feet right out from under him. Or I'll grab his head mid flog and gain control over him so I can cuddle him into submission. My great grandma... she did the head grab too, and it ended in a quick swing and he was dinner. Grandma didn't play around mean roosters. Then he got carried off by the feet, but he didn't exactly have a way to protest seeing as he was already taken care of. She'd do that with all the other chickens watching, if one copped an attitude during morning feeding. There never were that many mean roosters at great grandma's house...
