Except for the expense...
... the other problem is that the C-17 apparently simply isn't that good at all that rough-field stuff. It can apparently land in a short distance more or less as promised in ideal conditions (though according to one critic, not confidently enough for them to try to land on a real short runway), but not otherwise.
Just to forestall objections, IMO there is a difference between showing examples of landing in 1000m on a 3000m runway and doing the same landing on a 1000m runway. The latter demonstrates the ability as robust, while the former merely suggests the possibility.
It is the same as with tailslides. Russian fighters do tail-slides in airshows, and Westerners would then say Big Deal and swear they have seen a F-15 or -18 do a workable tailslide. I believe them on the working tailslide thing, but there is a huge confidence gap between doing something regularly on airshows and doing it quietly where no one would hear if you blew it.
In both cases, one is putting money where the mouth is, and one is not.
Other problems include a overly high ground pressure. In fact, the C-17's Aircraft Classification Number is higher than the C-5 (and roughly comparable to a An-124 at full load) even though both are much heavier aircraft carrying more load! The C-17 is apparently a threat to tarmac, which doesn't bear optimism on its ability to stay "afloat" on a rough field, and apparently starturns on rough fields are a no-no - too much weight, too much FOD!
For some extra (not so positive) information on the C-17, try this blog:
To be honest, I just discovered it last night. It might be controversial, but such blogs always are.