Here is how a mount system could work in FFXIV.

In line with the Armory System, a mount system could work in such a way that the mount you are using determines your class.

For example, if you are riding a Chocobo, you are a Chocobo Knight, and if riding a Dragon you are a Dragoon.

Yes? no?

As an aside:

An unrelated system could be applied to DoH or DoL who need extra inventory space. For instance, suppose that they could have a Chocobo Pack Mule that auto-follows them around and allows them to have extra inventory space.