I imagine it would take quite the overhaul. It could be cool, but it could also be done very badly, and make some combos all the more powerful and imbalanced. A lot of the things you have to switch pets to take advantage, become all the more overpowered.
For Example: Tiny snowman + kun-lai runt out at the same time? Make sure that your snowman is faster, and you have a round one stun. It would definitely add a LOT of depth in strategy, as well as making different breeds more desirable to game the speed of the pets.
I am really curious to see how it changes expansion to expansion. Will pets get a level cap increase? Will they implement new types of battles like 2v2? new abilities for a new level cap?
I've been really excited how they've handled each patch so far, and am looking forward to the elite pets in 5.2!