I will always return to the memories I've had and won't ever forget from the various Avatars that I've used over the years. Ranging from my Dog, to some random one I will never want to forget about but sadly did, to various Blastoise ones over the last year or so and especially the unique memories that the servers I've shown them in have given me with all the jokes and pranks.
But what would be really cool for me, would be making it possible to use my Avatars as backgrounds for the app which occasionally appear at random times, but for the rest of the time, the app uses it's normal themes. Perhaps even present them on particular milestones or celebrations of certain things?
Not least because the Blastoise I once knew myself as could return at any moment, but I just wouldn't know when, so it could be when you least expect it... Or you could just feed it cute pictures of cats and dogs along with cool and interesting facts, everyone likes those!