No reason to bring food. In fact, in most ports you are not supposed to take food off or bring food on the boat, even though lots of people pack a lunch off the buffet line for excursions, it usually violates the islands/countries laws to do so.
On RCCl boats, soda seems to be allowed, liquor is not, (wine is to some extent) but lots of people smuggle it in their checked luggage, (there are lots of threads about this on the boards).
Not all cruiselines are alike. I hear Carny is strict on bringing any beverages on board, but having never sailed on any other line, I cannot say for sure.
Most of the rooms have a small refrigerator in them with very expensive items, (like mini bars in hotels), but you can ask your room steward to remove the items, and use it to store your soda, etc.