The Elder Scrolls: Online

The latter is not entirely impossible, you can play as your pets in games like Mabinogi, TES could borrow that for added depth in a way the normal games don't get.

LotRO used to have a setting in which you could play as a monster. Your level was preset but you were able to modify your toon's appearance and attributes through templates, skills, and virtues. Battles there were much more chaotic there than in any other map although heroes outnumbered the player monsters two to one most of the time, and many resorted to camping spawn points for easy kills. It had its pros and cons but I'd say it was interesting enough in LotRO to be given a shot in another game.