In a case of a limited job, if they rework the limited job into a more interesting content and allows queueing.
In a case of a non-limited job, pets should be like the avatar of RPR or Egis from SMN. Only visuals.

Pets don't work in this game. And there is already 3 cases of pets:
-The dumb one, does its things then execute your order. Removed from MCH and SMN, limited to SCH.
-The Dot one, press and forget. Unfun and frustrating at times. MCH and DRK.
-The animation one, critically acclaimed, SMN and RPR.

Also, lore, weapon, relic name... It's alright to have ideas but is it really a priority?
Square Enix will make the choice about these, like how they decided Sage would be a gundam.