It's not landing on dirt that's the issue, it's landing on soft/soggy ground, and doing so again and again without tearing it up too much or ruining your engines. I've yet to see a pic of a C-17 landing on anything but hard packed dirt, which makes sense if you look at its published tactical landing characteristics:
http://www.wbdg.org/ccb/AF/AFETL/etl_97_9.pdf (especially page 35)
Based on that PDF, a C-17 can do only ~15 passes on a CBR-6 strip at 350,000lbs, which is equivalent to a roughly 44,000lb/20t payload, leaving 23,000lbs of fuel remaining for a ~500nm return transit. Let's round this to 10 mission cycles (since the take-off pass will be at a lighter weight) - still, the C-17 can only bring in 200t before the runway needs to be repaired.
By comparison, recent public statements claim the A400M can do ~40 cycles or 1,000t into a CBR-6 strip, with a 500nm return transit. That's FIVE TIMES a C-17, though it does seem to be less than originally planned due to weight increases (used to be 60 cycles/120 passes).
Then there's another problem with the C-17: FOD ingestion, which is much worse for a turbofan than a turboprop, and would make tactical ops frightfully expensive.