Here's something to consider....
http://www.wild-bird-watching.com/Feet.html
http://www.projectbeak.org/adaptations/feet_perching.htm
If you've ever observed a chicken's feet and how their legs and joints work at all you'd find they aren't much different than wild birds. They are
anisodactyl.....
and, though heavier than a typical wild bird, their legs work much in the same way to keep them on a perch. The tendons in their toes shorten when the knee bends, curling the toes. This helps them stay on a perch even when they sleep. Imagine the strain on those same tendons when the knee bends that deeply and the toes cannot curl...and the weight of their body is on top of that and they are like that all night long. Oh, they can do that position for mating, for sitting in a nest to lay an egg, etc. but to do it night after night on a flat surface is somewhat unnatural. You'll not see many songbirds sleeping on a flat surface for extended periods of time.
Because the toes cannot curl around the perch surface as they sleep, they must try to stay balanced in another way. Since the front part of a typical chicken outweighs the back portion, they must try to keep this uneven weight distributed on 4 inches of flat surface all night long, balancing upon their keels for the most part. Stress on the keel bone, stress on the flexor tendons, not enough good, restful sleep...is it any wonder people report chickens that pick at each other until they are bald? I'd be feeling the same way if I were those birds.
Add to that the the issue of "keeping their feet warm", which on a round perch positions their feet at the warmest place and into the warmest feathers on a chicken's body~right into the feathers of the brood patch~ and reduces the total area of the feet needing warmed due to the curl of the foot.... but on a flat perch positions those same feet on the surface of the abdomen and to the side of that "brood patch" area, with toes extended outward.
Here's additional information on how bird's feet stay warm in the winter months:
For the most part, frost bite on feet has very little to do with perch size and shape and much, much more to do with the right kind and enough ventilation in the winter months.