HEDP
Perfectly reasonable question.
I can supply a few 'reasons' why this is not done as often as it should be to make the user units a bit happier.
There is still a willingness from the operators to do this and it has been done recently, but overall the perceived impact on theatre ops is often a risk that the command chain is unwilling to take.
Sometimes, the user units won't open the airfields for an AT move or don't have the crash cat required. Additionally, especially the C17, doesn't have the flex in terms of availability to pre-position at a hub airfield. This would inevitably waste time when the ac could be doing something more valuable.
Sadly, the days of us being able to do as you suggest are gone. Lack of frames/crews/time makes it a non-starter on a regular basis.