I think it's debatable whether it should be called a "rule". It is one OF MANY DIFFERENT guidelines that are commonly advanced in various sources, but there is nothing that inherently makes it truer or more absolute than other attempted rules of thumb.
Frankly I am not happy with less than 10-15 sq ft per chicken indoors, plus run space -- because, having seen them at that density *and* (same individual birds) at 4-6 sq ft density, I gotta say they really do behave a lot differently and 'happier' at the larger space allowance.
But, it depends SO much on your individual circumstance, and if you live in an Eden-like climate and the birds are genuinely outside all day every day without fail, then all you're really building is a roost box and that doesn't take too much room; run space is of course a whole nother kettle of worms, but, same idea there.
Also, why do people keep saying that the "rule" is that you should have 4 (or 2, or 3) sq ft per chicken indoors and 10 (or 8) outdoors, without adding that it's a MINIMUM recommendation, not an ideal situation? Hmpf.
Anyhow, if you try to trace similar things back, and I betcha that these coop size numbers work the same way, it generally turns out that some gentleman-farmer Victorian pulled some number out of his butt when he wrote a pamphlet 150 years ago, and the number has been repeated and repeated ever since then, with suitable mutations according to each writer's own preferences. The thing to pay attention to, IMHO, is that many people over the years *have* found that sort of square footage to be workable. So, it is not bizarrely off, at least in terms of what gives you a reasonable chance of keeping chickens from becoming unduly cannibalistic too much of the time. Thus, irrespective of the origin(s) of the number(s), I'd argue that they do have some empirical validity.
Particularly if a person has otherwise-ideal conditions, and a rather relaxed attitude to how happy a chicken needs to be.
Hardly anybody on BYC (there *are* a few) are depending on their chickens to keep themselves alive or solvent, though. For upwards of 98% of the forum, it is a hobby, plain and simple (even if you do get eggs or meat or the sale of hatching eggs/chicks as a fringe benefit). On a hobby basis, I'd argue that it's a mistake to treat chickens as collectibles and see how many you can fit on the shelf. More space per chicken is kinder (and easier to manage!) than less space per chicken -- so perhaps the focus should be not so much on being limited by space, but rather on limitING one's collecting whims.
JMHO,
Pat