Well, we already know quite a bit about Ala Mhigan culture, and it wasn't actually based on 'Native American' culture, especially from 1.0, it was stated that the citystate was actually an autocratic kingdom, who had a long history of belligerence with the other Eorzean citystates (a century before ARR they attempted to invade the Black Shroud, which resulted in Gridania allying with Ul'dah and Ishgard to drive the Ala Mhigans out, an event known as the Autumn War), and, more so, was actually stated as being prior to the Garlean invasion and annexation, the 'most technologically advanced of the six Eorzean citystates' - yes, even more than the Sharalyan colony). Their military consisted of ARCs, LNCs, GLAs (knights), CNJs and THMs, but also the elite MNKs of the semi-theocratic order of the Fists of Rhalgr. In fact, the only reason Garlemald even managed to invade them was because their final king descended into tyranny, purged the MNKs and so weakened his hold on power his own people overthrew him, which when Gaius and the XIVth Legion showed up, there was little the beleaguered nation could do but watch helplessly as the Empire annexed them.
Minfilia is not a fighter, even in 1.0 she was a pacifist who actually preferred diplomacy and negotiation over direct conflict. In fact, there was one point in 1.0 where she actually tells you off for putting yourself in danger and resorting to violence instead of 'playing it safe' and researching information peacefully.
It's why she's the Antecedent, the head of the Path of the Twelve/Scions of the Seventh Dawn. She's their director, who sits in an office pushing papers or making business deals instead of going out into the wilds and killing stuff. As much as I would love to see the DNC Job added to FFXIV (it being one of my favourite Jobs), Minfilia does not fit the idea or image of the Job, as she doesn't even need one.