Will we, as white mages, be able to put on the hood at some point?

[Felis]

I don't see why it couldn't just act like a cowl, but hide whatever is on your head to prevent clipping.

It makes me extra sad that we can't because back in 1.0 when they teased AF there was a concept art image of the hood being flipped up.

Because every job quests give you 5 AF pieces.
With a hood, WHM would only get 4 AF pieces, give them a disadvantage (less gear rewards from the job quests).