The military actually does run it's own movie theater chain. I'm not sure who pays for it, but the showings are free. Although I think the movies are released a month or two after the normal release date. And I doubt that the military actually has a theater somewhere in Iraq or Afghanistan
Actually a lot of the bases had movie theaters in Iraq and Afghanistan (not the little 10-1000 person bases, but the big ones like Balad, Bagram, etc. which have >10k people).
It also must be much harder to actually watch reel-to-reels. You can just pop a DVD into any computer at any time without worrying about the additional logistics of space, trained projector operators, and time constraints.
I was a protectionist during college and your number one enemy with film is dust and dirt. I would imagine the prints would be unwatchable after a dust storm in Iraq.
do people actually refer to celluloid movie prints as "reel-to-reel"? i suppose the term is technically accurate, but i've never heard it used for anything other than the pre-cassette magnetic tape audio format (or i suppose very occasionally its data-tape derivatives).