Based on the text of the wind-up Kain minion, we know that Kain existed in Ishgardian legend. And I think most would agree, it would be cool if Dragoons could ACTUALLY fly.
Even if the mount itself could be used while other jobs, I would add a quest which ONLY Dragoons could embark on, acquiring a lance or spear to harness the currents of the wind, allowing Dragoons to soar through the sky!
Could maybe even tie it into a revamped Garuda or Nidhogg fight, or something like that? Make it a bit of a "status" mount though, not just GIVEN to you for leveling a Dragoon.
Just my two cents!