Losing is definitely a mechanic I want to have. I've always enjoyed the loss scenes in these types of games more.
I'm hoping to have a sort of rivalry budding with these scenes. Characters progressively going further in the loss scenes as you lose more. The inverse of this is having characters get more competitive with stat buffs/different AI as you beat them (Also to make sure you can't just steamroll the same fight multiple times with the exact same moves since the AI is not random)