It would be very interesting to have global information about other players on daily challenges. I know it is a new thing to collect information from other players, and it also implies an internet connection and so on....... BUT. 

It would be very nice to see how many players got to play the daily challenge, how many completed it, and at which time (average), etc... it would be a great accomplishment to complete one that almost everyone dies. It could give a nice touch to the game and create even harder challenges.