USNA uses demilitarized M14's. Back in my day we used demilitarized M1 Garands.
USxA is not a combat posting. As such, there is no need for functioning weapons to be present in the hands of Midshipmen/Cadets. Additionally, the only means available to secure these weapons is a cable lock in the Mid/Cadet's room, which is totally unsuitable for a real weapon. Also, having 4,000+ real weapons so flimsily secured would make USxA a prime target for theivery of items we'd rather not see stolen. Finally, "they aren't loaded" cannot be guaranteed when some stupid kid decides to go buy a box of .308 Winchester and get a magazine from CTD.com, then load the puppy up.
Now, one can argue that a military establishment should allow it's troops to be properly armed, and that may be a debate that needs to be held, but the reasons why the current situation exists are as mentioned above.