Good point, the coaches/players. nytimes article on the subject.
http://www.nytimes.com/2011/10/18/sports/football/ipads-repl...
And these are just a few reasons I can think of. There's nothing but benefits to this policy and very small negatives.
It's analogous to filling the moat before a battle. It's just a defense intended to slow an enemy. Try to remember that these guys are some seriously strategic thinkers, they're not morons and they're not technophobes.