Wouldn't it be cool if your Chocobo could interact with you more?? Yes they do fight alongside you and you can change their color unlike other mounts, but other than that, they don't really feel special. They're supposed to be your "companion" especially when you're new and at a lower level, but I think most people at any level only use them as a tool for extra dps or for the regen.
I think giving them extra interactions would be so cool and give more life to them. Eating out of your hand, doing a periodic whistle (partially whistles the chocobo theme or similar), dancing, sitting/sleeping with a player, reacting to emotes, and interacting with other chocobos are a few things I think would be awesome to see.
With these or any others, I think new players (or anyone) would get a lot more out of their "companion", and in general, they'd be more fun to interact with!