My suggestion is to make minions remain out while your chocobo companion is out, while riding chocobo (I understand not flying), and most of all.. in duties! (I even understand if they can't go to 8-mans, though I'd be sad; it seems silly to not allow them in 4-mans however.)

When I started the game I fell in love with my fledgling dodo and was disheartened when I couldn't summon it in duties. I was further saddened to find I couldn't have both my dodo and chocobo out at once. This basically resigns my minion to being out in main cities (as long as the chocobo isn't in my party still).

I'd love to be able to see what pets other people like to use, as well, and I think this would build a stronger emotional attachment to the minions as well as the game as a whole.

Please let me bring my Fledgling Dodo along on my adventures.