The problem with the GCs is they're now somewhat bereft of purpose - their original lore and gameplay reason for existing was for the original version of FFXIV (1.0) during the run up to it's shutdown, as a means of consolidating the citystates resources and manpower to better face the impending Garlean invasion (before that point, the citystates actually did not have proper standing armies, they had token militia forces that were just glorified police forces and not much else, it's why the whole adventurer system was formed in the first place), specifically, mobilizing for the looming final showdown with Nael's VIIth Legion on the plains of Carteneau.
Post Calamity however (i.e., in ARR), when Gaius's XIVth Legion turned rogue, the citystates drew back and concentrated their efforts on rebuilding rather than warfare. Before Stormblood and Ilberd's false-flag operation on Baelsar's Wall, the only real major engagement the GCs did was Operation Archon, and even then it was more just support - as the player's character and their allies did most of the work.
So since the start of ARR the GCs have been content in search of a need, there is little lore behind them now sadly, they're just the volunteer military force for each citystate with mostly mercenaries and adventurers in their ranks and not professional full-time soldiers.
I don't really see this changing either, given the player's character has been increasingly more involved with the Path of the Twelve Scions of the Seventh Dawn than their GC. And with the aftermath of SB
liberating Ala Mhigo and Doma and thus finally giving Eorzea some much needed breathing space from the threat of Garlean invasion for the first time in over two decades
, they're becoming even more superfluous unfortunately.