Football is different. It is timed everywhere, there are so many people active at the same time, it would be too difficult if the information wasn't made available.
I know we have worked up to this modern coaching style over quite a few years now. Baseball is a series of generally one on one match-ups with a fairly fixed amount of options and actions that can occur. I know they are now introducing some timed situations, but if they just eliminate those 5 to 10 seconds of the coach sending in the pitch to the catcher then him relaying it to the pitcher the game would speed up. I know it takes a burden off the catcher, but he can see things they don't see from the dugout on how the hitter reacted to the previous pitches. Drives me nuts when a batter obviously can't catch-up to a fastball from a pitcher and the dugout calls a breaking ball or vice versa.
Also we now have all these arm bands or fanny packs and players looking for a signal between every pitch then looking at their arm band or fanny pack is just too much. You should know the situation. Glance at the coach and if he wants to do something then look. There was no reason for me as a hitter to look at third base with a 1-1 count, no one on, and 1 out. And there are a whole bunch more situations like that in a game.
Polkie always said the first 6 innings were ours and the last 3 were his. We were prepared for each situation that could occur and did communicate it with each other. It was pretty rare for the coaches having to get your attention and reposition you or totally change your plate approach.