Unless they're PPS (Peter Pan Syndrome) in which pets stay in the "child" state forever! Yay!
Also, I find clickable ones really annoying, and I'm sure lots of others would if you had to click on all of your pets every day and ask people to click them, and then you can't get back to your page without undoing your click... It would make it really annoying, and not that inviting as it is now.