Well unspellable, you actually answered your own question, if you just give it a little thought. The fact is when you load those little round shot "Each & Every" one of them have air space around them. They don't fit in tight like those cubes in the Rubik cube. Present day Hornady (Formerly Bair/Pacific) charge bushings are listed by their dia, all being 1.0" long. Fomerly the dia of their shot bushings were also listed. A 1¼oz bushing was listed as .664". (16ga = .662"). Note however this bushing is 1.0" long. The sq load in a 16ga would be only .662" long. .662 x 1¼ = .828oz.
This calculates out to .277 SqIn per oz while Alliant's figures work to .288 SqIn per oz. A slight variation probably attritbutable to a different size shot or different alloy or both being used. A .662" dia cylinder x .662" long however has a volume of .228 SqIn. It will therefore hold nowhere near an oz of shot., closer to 13/16oz. The loads I am aware of that come closest to being "Square" are the old 1¼oz 10ga load & the British gamegun load of 1 1/16oz. Funny thing is I have never seen either of these loads bragged upon because they are Square. Usual references is to the 1oz 16ga & 3/4oz 28ga loads. Neither are actually square, one is a Round ball equiv & the other is neither. A 28ga Rd Ball equiv is a little over 9/16oz & the Sq load just over 7/16oz.
I cannot recall ever seeing anything by an ammunition Co or "Real ballistician" even mentioning a square load. It is uaually some one trying to "Build Up" their personal pick of gauge. The hillarious part is all the "Proof" they go through, if it actuall meant anything at all would have just "Proved" their choice totally worhtless. Fortunately for those who like different gauges (I like them all from 28ga up) They are totally "Non-Dependant" upon a sq load.
Each step up in gauge though gives a little more versatility in the loads it will handle & allows for heavier loads to be used. All of us though may not need the maximum possible loads & each person just needs to decide what suits their purpose.
But again there is "NO Magic" bore size Nor is there any advantage to a SQ load. Personally I see no reason at all in "Magnumizing" the small bores. 3/4oz in 28ga, 1oz in 20ga & 1 1/8oz in 16ga are all fairly heavy in proportion to their bore dias, & as far as I am concerened their working limit. Even these are more appropriate to modern guns capable of handling SAAMI pressures. For anything more I prefer to step up in size, rather than using continuously longer shot columns in a smaller hole.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra