I would think so. If personnel aren't stable enough to carry - then why are in the "Armed Service"?
I think some of the leaders are afraid of retaliation for disciplinary actions, therefore, everyone must be unarmed. That's exactly what the left wants to do more broadly, and will do if given a single inch of wiggle room.
None of the Armed Forces have enough sidearms to issue to each soldier, sailor, airman, Marine, or Coast Guardsman. Most of the firearms on hand in the military are select fire rifles/carbines (M16, M4, etc) or machine guns, which are inappropriate for general carry.
The military leadership’s reluctance to permit carry is related to risk aversion. While there have been few instances of blue on blue violence in Iraq or Afghanistan, where almost everybody carries,there have been a couple. IIRC a soldier shot up a clinic in Baghdad back around ‘08 or so.
In garrison, commanders are harshly judged on soldier misbehavior, which generates training related to eliminating DUIs, domestic violence, etc... I can imagine he stink if a soldier armed under this policy committed a crime.