The HoS could have reason to go to the armory either to put more stuff there, or when issuing a weapon permit. But most of the time such weapon permits are getting things from science, such as stun revolvers. There's also the ARMOR in the armory, both the exceptionally useful shields and various forms of body armor for brute attacks and energy weapons, and you could easily hand them out to someone who's going into a dangerous area. Hmm ... a lot of this seems to come down to the idea of don't do things without a reason. Don't steel all the guns just to have all the guns, don't arm and armor yourself to the teeth if you plan to sit in the bar and drink all day.
To that end having a reason doesn't mean that there needs to be some emergency requiring active defense to shoot at monsters or pirates. "A reason" could be as simple as testing out a weapon you haven't seen before, giving weapons and armor to someone else so they can test it, thats what the shooting gallery is for after all. And science sometimes appreciates being given parts and weapons from security to make upgraded things, at which its faster to hand them a spare gun we have on hand and then call cargo to re-stock, than it would be to leave the armory un-touched and have Cargo handing out the guns. Only for security to have to get involved anyway because they have to rush down and unlock the weapon crate. Normally. Sometimes scientists and cargo already have a means to open the crate and they just stay quiet about it.