Water has a much higher heat capacity than water, and obviously much higher density too. By filling freezer space with water, the thermal mass of the freezer goes up, and it will stay cold for longer in a power outage.
I keep soda/water bottles in a secondary downstairs freezer. They're my ice packs for throwing in coolers. (This, of course, makes more sense if you have more than a primary refrigerator/freezer).
Small fridges sometimes have an icebox inside them, which is a different thing to a fridge/freezer which actually has a separate door, or a dedicated freezer. The icebox is just a part of the fridge compartment, weakly insulated from the rest of the compartment, and the cooling plate is located inside the icebox. The rest of the fridge is kept cool mainly from cold leaking out the icebox.
