I think the thing I've noticed since playing pretty much exclusively classic for the past year is that oftentimes I will load in to a game, see unrated lobbies and have no idea if they are new to the game, new to the mode, or a smurf.
I think showing player level is a potentially good way to counteract the rank based aggression (flame for ranks etc) and instead shed insight into how experienced the person is in playing the game through the levels.