Why would the USAF have no support for autolanding?
FWIW, I do not fly the KC-10, but I do have friends that do...

Anyway, you're looking at a T.O. that is 7 years old since the last change (not sure when the most recent write-in is)...  Military pubs are always changing, avionics upgrades are always happening, and what you're looking at may be severely outdated.

Having said that, I don't believe in this instance that it is.  However, I don't see the need to be able to shoot CAT IIIc approaches.  What does the Air Force gain?  Once deployed you aren't going to have that technology, and CONUS you just divert.  So why spend the money for it?

I may not know the full politics behind it, but I do not see the operational need for it.