I think that there actually are places to go, that young people know about and I do not, where one can do exactly that. Shop for avatars. If not, then it looks like it would be an interesting idea for a biz, on the surface, if you could get people to pay for them, or restrict usage in some ways. ( Some people might want to have "exclusive" avatars that no one else has; just like women going to a party supposedly are disappointed at seeing another wearing the same dress- is that true, by the way ? )
The avatar you are seeing right now is from an old "golden age" comic book that used an artist I liked for its covers, whose work was influential on later cartoonists. Another comic book cover by the same guy is my avatar right now over at INTPc. He fit into the Halloween theme. See also my thread "Pontookers".