Also! There's a few (very few) FF games (and Bravely Default which is a FF game in all but name) where Aero is part of White Magic so it also fits in with the CNJ in XIV.

I'd also like to point out that it's the BLM soul crystal which prevents the user from burning up from channeling all the excess aether, not their staff, but the staff itself is also a focus on Thaumaturgy (and Conjury, for that matter) without which the spells would (in theory) be wild and, heh, unfocused. If you notice, our spells seem to come out of our staves (THM animation literally shoots them from the tip, BLM channels from the staff even if the effect happens a few malms away) so, while theoretically possible, it's by no means recommended.