Cooking equipment is sort of like camping equipment, IMHO. You can make it without carrying either, but there are going to be some nights when you're really, really glad to have it.
We normally broke out fast with oatmeal, cocoa, and Poptarts. I quickly learned that was only good for 15 miles or so. The problem I see with your plan is that there's stretches, particularly in the west, where there really isn't a place to get supplies (be it one of those ghastly bacon, egg, and cheese biscuits, or a real breakfast) for many miles.
OTOH, we passed a couple who had planned out their entire NT trip and made reservations for each night, so I suppose it is possible. They figured they could average 15-30 miles extra per day since they weren't carrying camping equipment. So you could perhaps plan your trip such that you were always at or near a place for breakfast and supper, and carry lunch as needed.