But during the rest of the game, watch closely: along the sidelines you will very rarely see anyone using their tablets
Of course you won't, because right now you rarely see images of everyone looking at the photos anyway. But that's what these will be used for. If you are actually at a game, look at the sidelines and you will see an assistant coach by the bench holding a thick 3-ring binder. These binders hold photos taken from the coaches booth near the press box and show the other team in different alignments. With tablets allowed on the sidelines, instead of having someone run off a bunch of photos they can just be pushed to tablets on the sidelines. Depending on NFL rules they may even be able to push recordings as well. Players already spend hours each day watching film, if they could I am sure they would study film during the game as well. Since teams always tweak their game plan depending on the characteristics of their opponent, previous gamefilm can only tell so much.
And have you ever watched/attended a game and seen a large dry erase board on the sidelines? These are used to draw up or adjust plays on the fly. Generally the offensive or defensive coordinator will call down to an assistant and have them draw up the new play for the players to see. Using tablets the coordinator could draw up the new play himself and simply send it to the tablets the players have on the sideline. This could also allow for animated playback, showing the players how the coordinator wants the play to develop without having to draw more lines than John Madden having a stroke.
Then there is also the fact that for challenges the referees already use a hooded screen. They aren't going to be standing around in the middle of the field holding a tablet.