He knows some troops would literally just go and kill their commanders.

I'm not sure this works how you think it works. Military members aren't prohibited from owning guns, they just have to store them and check them out to go shoot. There's been plenty of shootings on military bases with personal firearms because unless you fully search every car coming in, you won't stop someone from bringing one in.

If idiots are carrying around off duty it's more likely to cause a drunken bar shooting than a fragging incident.

Also also the memo literally says it'll let everyone "request" to carry, implying some level of commander is the one to approve it.