Over the years I have concluded that most writers praising the square load have not the foggiest idea what it actually weighs for any given gauge.
Also they nearly always give the British credit for it.
Fact of the matter is the 12ga 1 1/16oz load came about as an act of parliament & not by a ballistician. 1 1/8oz had been settled on as the Standard game gun load. When WWI began for the savings in lead Parliament restricted the load to 1 1/16oz. This resulted in a savings of 1 pound of lead for every 256 shells loaded. Aft6er the war with the restriction lifted many stayed with the load as they liked the reduced recoil, though some went back to 1 1/8oz. I seriously doubt its being square or not had any bearing on either choice.

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