TSA's statement about food in checked baggage is a suggestion, not a rule. They suggest you don't bring food because food can slow down the baggage screening process *if* the food in question is dense, because dense foods can mimic the appearance of plastic explosives on the scanners, which necessitates a manual search.
The airlines have rules about foods in checked baggage, too, mostly barring glass containers, perishables and any kind of ice, because if baggage is lost, spoilage can cause real nastiness. Dry ice is forbidden on aircraft (except when used with special licensed shipping containers) because it can explode. That said, liquids CAN leak, so if you pack them, always pack them factory-sealed, in an outer sealed wrapper with an absorbent filler in-between to soak up anything that does leak out.
I checked a soft-sided cooler at MCO yesterday. We had just left BB, so it contained a super-large doubled ziploc full of sand shoes & damp swimsuits rolled in towels, and also a couple of unopened bags of chex mix that we had left over. The agent joked that she was disappointed that it wasn't full of food because she was hungry, so I told her that she could help herself to the crackers with our compliments. The Chex were both still there when I claimed the bag, and the bag had not been opened.
I almost always have a 20 oz. coke and a similar-sized bottle of water in my "personal item" bag when I fly. I always take them out and put them in the seatback pocket for the flight itself.