Personally I wish leveling a Chocobo was marginally better in terms of experience gain. Things just take too long and I gave up after Rank 3.

Not to mention the pet combat system for the Chocobo is really stupid. Either my Chocobo refuses to attack (even after changing its stance to defensive or free), or it takes its time getting to my target.

Honestly, I'd say improve Chocobo leveling entirely, remove it, or allow it to level along side the player.