In the event of an accidental/negligent discharge, they might look bad to the higher-ups. The best ass-covering move is an outright ban.
Been there, done that. Vietnam era through early 70’s pay officers carried personal sidearms as it was easier than hassle of drawing from the arms room. Lots of souvenir pistols from RVN at that time, I carried mine. Then they cracked down.
Historically, personal sidearms were permitted if chambered for the issue service cartridge.
Joined National Guard in 1974 & most officers carried their own sidearms in the field. Somehow that all got swept away as MPs & CID were simply looking for excuses to bust people, IMO.
If a soldier or officer meets the standard for concealed carry & has commander’s authorization to carry based on need, then by all means make it happen. If Achmed & Hassan don’t know who’s packing on post, then it becomes a safer place.