In one of the older 2k football games (2k5?), they had a weekly wrap up with Chris Berman running down scores,stats,standings,etc. ; I think this would be a welcome edition to My League or even My Career. IMO it would definitely make the experience more immersive.
One of the older NBA 2K games (I want to say 2K10) used to sometimes show a ticker at the bottom of the screen with stats and fake MLB/NHL scores, I thought that was a cool little feature that added to the TV presentation feel.