We're starting to conflate some related concepts. A squared up stance is useful beyond use of body armor because it gives you a good combination of stability, good area coverage and movement. This is why it dominates competition shooting that involves moving and shooting simultaneously.
I'm sure people who have a need to shoot on the move at close proximity targets in armed conflict also wear body armor whenever they can; but I'd be willing to bet that mobility is the main driver of a squared stance, not armor.
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