This is a problem indeed. I must admit I didn't think of it when writing my post. My proposed solution would also solve this problem, as the pet controller would essentially be a cheerleader in battle.The biggest problem with pets in my experience isn't really balance, although I grant that can be a problem.
The biggest problem with pets, steeds, summoned creatures, henchmen, minions, etc. is that when the PCs become a small army instead of a squad of commandos it massively slows down play. I groan inside whenever a player wants to play a concept that invests in minions of any sort because that one player's turn can take as long as the entire rest of the party.