I've done it a few times to level up Chocobo Companions. There are some good "camp" sites as you level up across multiple zones, and Chocobos can fill in for a Healer and/or a DPS if they're built right.
The problem is going to be maintaining EXP skillchains - you can get to about chain 5 or 6 solo easily enough, but for any more than that you need good pulling coordination and heavy AoE damage.

It's always going to be slower than grinding fates or leves, but there's nothing to stop you doing it in-between fates...