I won't entirely disagree with you on the space requirements but I do think it is all about perspective. My first coop was an A-Frame with a 4x4 footprint and 4' high too. It had an attached 6x4x4(h) run that I didn't use at first (I later set the whole thing up as a broody coop/run and it worked fantastic for that but that's a whole 'nother story.) Anyways.....the original coop was where my chickies slept at night. During the day they free-ranged the entire backyard. The coop originally had no roost (It was given to me off freecycle) so I installed a roost as high as I could go while still giving them head room. At one point I had 9 chooks and they ALL slept in that little bitty coop with NO issues. With a 4x4 footprint, I shouldn't have had more than 4 birds in there but 9 had no issues. Why? Because ALL they did in that coop is sleep. Their food, water, nest box and free-range were elsewhere. During the day they had plenty of space and at night all they were doing was piling onto the roost and going to sleep. In fact, I would venture to say that they were warmer in that coop during the winter than in my current, much larger space, because being so close together and having limited space to heat, they could keep it toasty warm. I even experimented by moving their water bowl in there at night one January and it never froze, even in single digit temps. I digress...
This is NOT to say I am recommending going with a smaller space. If the range during the day is limited, you will have issues cramming birds into such a small space. My set up only worked because I wasn't using that as the space for food etc. Part of the "4-square-foot" rule takes into account space needed for nest boxes, feeder, waterer and so on, which mine did not have.
The last thought I will leave you with is that crowded birds end up being stressed birds, and stressed birds typically have a lot of "issues". You will hear about problems integrating, bullying, feather-picking etc. I never had those problems but if my girls weren't out free-ranging all day and were confined to that 4x4 coop and attached 4x6 run, I might have experienced those things even if I had half the number of birds.