I'd rather not include unique actions like these for in combat or dungeon use. There are so many ways you can really screw up game balance that way, like ASTs rolling twice on loot. It would make all other players really angry if the AST got gear they "didn't deserve" because of a funky caveat.

Things like Bard's symphony, however, would be great. It would be nice if each job got something special that didn't have an impact in-game.

Summoners should get more Carbuncle colors, Egi glamours, and Demi-primal glamours.
Bards can continue to get music to play outside of combat.
Dragoons could get access to a baby dragon pet which they can care for and use as a mount after maturity with some customization options like with the company chocobo.
Astrologians could receive a tarot reading mechanic where you could do tarot readings for other players or yourself.
Scholars could get access to faerie customization and be able to change their faerie's colors and hairstyles.
Ninjas could see a number of secluded spaces get added to various spots in the game only accessible to Ninjas via teleporting. These spots would just be cosmetic.
Machinists could be able to customize their own housing furniture and things placed in their rooms, houses, or apartments.

Stuff like that.