Would it be possible this SOP was instituted back when 5 rounds was a full clip (for a 1903 Springfield)?
One of the reasons that the British forces at Islandwala were defeated and massacred was that that the ammunition was not ordered to be broken out, and it was very difficult to get at.
It sounds as if things are much better today, in terms of trusting the troops. The all volunteer force is very professional. Back in 1976. I still had a draftee under my command. He was one of the last ones. A really excellent soldier, you could count on him, and he would get the job done right. Moral in much of the Army was low, after the defeat at the hands of the U.S. media... oh, I mean the Vietnamese. Now we have perhaps the best military in the world, but moral is probably in the pits with the current Commander in Chief doing his best to depress it further.