I did contract work on a base, and a couple of the vets I talked to told me that the Army/Navy was/is afraid of fights boiling over into gun fights.
The fights and pulling/getting weapons occurred back in the early 70s when I lived in the barracks. There were more than a few incidents although most were kept pretty quiet. I was personally involved in jumping on a drunk guy who was coming back into the NCO club to shoot a guy he had a dispute with. He wasn't the only one. Even then, our service weapons were kept first in the barracks armory and then in the base armory. I don't know what the Army did then, but having gone to a joint school on a large Army base there were several fights that eventually led to some attempted or realized cuttings from soldiers using their bayonets. Today, I might see letting troops open carry on base but even then, drunks, twits, and love triangles will be problematic.
The ban has been in effect for a long time. I believe it was put in effect shortly after WWII.
For most of that time, installation commanders had the discretion to make their own rules on the carry of arms by soldiers.
There was a real problem with moral after Vietnam.
Now we have an all volunteer, professional army. They are very good. A cheap way to increase security, without political blowback, is to allow those that take the trouble to obtain a concealed carry permit to do so.