As it stands right now, when you complete a quest with companion gear as a reward, you pick the one piece that fits the companion you've been using, and you go about your day.
The problem comes when you want to use a different companion and, unfortunately, you've only been choosing 1 companion's gear to keep it up to date while all of your others have nothing new.
Would it be a big deal to get all of the companion gear when you turn in the quest, so that all of your companions can be caught up gear wise while questing? Maybe even have the reward be a companion bag (boots), or Companion Bag (chest). That way, if i have been gearing up bowdaar, and want to switch to Risha for some added dps, she won't be sitting in worthless underleveled gear.
I feel like, at worst, they would take a lot of bag space, and, at best, you would be able to choose any companion and have them viable throughout the leveling process.