On one of my trips to Viet Nam I went with a unit on a military aircraft. We were authorized to carry a personal fire arm with as long as it was listed on your individual military travel orders by make, model and serial number. I carryed a S&W model 28 (4 inch, .357) with a box of FMJ ammo. I knew I could get .38 in Nam, so there would always be plenty of ammo available.
Like sourdough, I also spent 24 years in the Military, most in the Air Force. When the military went from using military aircraft (in most cases) for moving troops they stopped the practice of carrying personal firearms. Most military personnel today are moved by contract airlines, often landing at civilian airports both in the US and overseas, so carrying firearms of any type by an individual is rare.
In addition to my military carreer, I also spent 26 years in civil service working in the aircraft and logistics field, during my military and civilian service, it was rare to see an NCO other than a security forces member with a sidearm. Most still carry the little black gun. Working logistics, and responsible for the deploymment of military members for the past five years, I don't recall ever processing an individual with a personal firearm.
From my experience, most enlisted who have a sidearm in a combat area, and are not in one of the areas where they might be issued, obtained the gun by, in most cases, some method other than the prescribed method. (picked up off the battle field, stole it, bought it, etc.) This was "common" in Viet Nam, but no one seemed to care. We were picking up wounded after a fire fight in Nam, While waiting for the Med Evac Choppers to be loaded I picked up a Thompson. Three months later the Army CID called me in and questioned me about it, I admited I had it, their response was OK, we just had to account for it. I didn't know, but a battlefield recovery group has already addied the gun to their inventory list. They traced it to me by process of elimination and talking to all the aircrew members that had flown into the site after the battle.