All mounts would definitely be a pipe dream.
But I'd like to think they could expand the companion system a bit.
Maybe introduce Beast Tamer as a limited job that uses the companion system.
BST would have the ability to tame certain mobs to add to your companion roster, and BST itself could call them in instanced duties, probably with special command skills. But outside instances, you could call those companions as any other job just like the Company Chocobo.
It would be a neat way of adding a limited job that also contributed to the wider game experience, instead of being entirely isolated.