Given my distaste for the new mounts system - that is, the apparent lack of restraint and/or taste in what'll be available (Ahrimann? Red XIII? Seriously?!) - I'm extremely glad that the chocobo companion system will encourage people to favour the iconic birds.
Besides, if they made the companion system open to the other creatures, it'd only result in their having to remove a lot of the deeper elements, else every new type of companion'd necessitate new barding models, new layers to the breeding system, more balancing work, probably new AI work...