I'm pretty sure that ship has long sailed - at one time the development team did plan to have other mounts like the legacy chocobo available as a companion fighter, but ultimately the plan was dropped - presumably due to balance issues and the fact that the company chocobo can equip barding and trying to balance that with other mounts would have been too complicated (the legacy chocobo for instance would have lost it's unique look if that was the case).

And given that we're going to be able to use our adventurer squadrons as npc fighters in dungeons and the like in Stormblood, it's even more telling this sadly will probably never happen I'm sorry to say.