The most basic, and probably cynical, reason is probably because this won't improve performance at all.

Squadron AIs seem to operate on an VERY simple AI Roulette with just a few modifiers like healers prioritizing esuna way too much or melee DPS missing 3 GCDs just to land a positional. I can easily see MNKs formshifting at random. Squadrons also lack cooldowns for whatever reason, and it may not seem obvious now, but it'll be noticeable by everyone when a WHM uses assize every 15 seconds. Personally my favorite was my WAR who kept alive at 1 HP for 20 seconds by spamming holmgang.