No idea how they managed to extract, sort, and move the bags between holds at Atlanta
If the civvy world can manage to do it as a matter of course then clearly it can be done
They mark them as such, they put them in the Sort Tin and they get handled as the minority exception and are expedited as such when you hit the hub. Easy.
You are comparing two totally different things - transiting through a hub with connecting flights and getting on a flight to an operational theatre. Nice schedules with enough serviceable aircraft available would be lovely out of Brize - but it won't happen for a plethora of reasons.