I have 4.8 square feet per bird in my coop. They were happiest when they had 9 square feet of space in the coop, not counting run space. Can they survive on less? Yup. Can they be happy? Well...
Whilst I see no reason to confine and coop up birds any more than you possibly have to, even in the name of chicken math, it's your choice. Climate definitely has an impact—I live in a very snowy and cold climate, so, my birds would go nuts and so would my cleaning time if I tried to keep them cooped up with 1sq foot of space each for as long as I have to every year. They free range in summer but there's still half of the year the snow is too deep for them to go out in. I don't know about you guys, but I am not shovelling my yard for them!
Also, I think that having multiple levels is the only way something as low as three or four sq ft CAN work. Birds are birds, not windup pocket pets you can box after you're done playing with them. My coop is 12' x 12' and I have about 30 birds in it. Most of them are LF hens/cocks, but 9 are ducks and 3 are bantam chickens. I do not have bully birds, but they definitely have their squabbles and require space, levels, and judicious removal from flock to remain happy.
I cringe when I see chickens kept in a dinky little prefab size coops, just like I cringe when I see horses kept in a corral permanently or goats stuck in a box stall. And people wonder why their animals have health problems.

Just my take on things. Good luck with your birds!