Why the heck should I waste a good 30 seconds to log out and back in to leave a poor pet for someone else? There's a damned good chance that "someone else" who's running around that spawning area is a rare hunter just like me, and in an effort to be courteous I've let that person get into 2-3-4 pet battles and get their rare, while I get stuck with nothing...again.
No way. If 99% of the population are going to say "me first!" then I have no choice but to do the same. I've spent the last 6+ years standing back and being courteous, and it get me nowhere.