Typically freezers have defrosters in them to prevent them from building up too much frost because it can damage the unit (water is the only element that expands when freezing) and if you let the ice get to the edges it will burst the sides or destroy the freezer walls.

If you had very large ice-cube makers this would probably be your best option. You can or could stack the blocks right up to the edge of the freezer since the water is already finished expanding and then you could have them fill up the whole thing, top-to-bottom, but then you have to deal with drainage issues after/during the fact. Chest freezers have a drain at the bottom, but it would have to be on a surface that could withstand the water (such as a patio, mud room, or garage with a drain in it or a way to pipe the water away from the unit).