I think it would be nice to be shown some stats about the game after it finishes. The stats could be displayed in the chat box, and would consist of information such as EXP gained, awards achieved, total damage taken/dealt, C/U/R cards drawn/turn and so on.
I know the battle report already exists and I do not mean to replace them, but it would be convenient to view the stats in the game window. And, of course, it can be optional for those who don't want it.