Actually, MREs still contain paper, damp resistant matches (against humidity, not submersion). And you're still issued the canteen cup and canteens (canteens have an NBC mask adapter hydration systems don't). If, theoretically, you were actually carrying your canteens and the cup, everytime you get lunch you get the means for lighting a fire and having a brew up. I think the main reason we don't is operational security and logistical support. If you're out traveling light, you don't want flame and smoke giving you away. If you're not, someone generally comes around and feeds you and brings insulated containers of coffee and what have you. Or you eat in a giant FOB dining facility.

Oh, and so many people smoke in the army, if you can't find a lighter to get a fire going, you should be more worried your smokers twigging out from lack of nicotine.