Now you've got me curious ? I can say for sure that in the last 10 years I've never heard a USAF transport (C-5, C-17, C-130, etc.) use "Air Force" in their callsign. Plus I can't recall ever seeing any transports identified by Axxxxx on ADSB-X. Can you give me more context on where you are hearing this and seeing Axxxxx ?
We see them in Southern California on a somewhat regular basis, but then again, there is also a ton of military stuff that goes on out here. We see Army (R) use the numbers a lot more frequently, but definitely see it out of the Air Force as well.