Yes, I would love for a mini game, pokemon style battling (like what wow has), minor buffs (like what Runescape does), or even something as simple as the pets being more interactive like being able to pet them, make them dance, have them point or be used as a pointer, or make them fetch things (toys not loot, although loot fetching would be nice too). They are just so small, and hard to really see a stand out one that someone might have following them. Unless there is a reason for a player to actually walk around with or use them they'll likely be hidden numbers to know how rare a pet really is since no one will know how many active players got in on that promotion, or got it as a drop off of X, or spent $$$, etc.
Those are just a few ideas and reasons, I think this would help flesh out the more causal side of things to chase in game. I love having little things to do, but pet collecting with nothing but them standing around just doesn't seem like an engaging thing to me.