Much of the food you place in the freezer will have a high water content, so if you keep the freezer full of food there is no need for bottles of water. The food  provides the "thermo-inertia" which your Dad recommends, and minimises space for cold air which falls out and is replaced by warm moist air at room temperature when you open the freezer door (unless it is a chest freezer).  

But if you are not able to keep the freezer full, it is an excellent idea, for the reason your Dad gives. You should fill as much space as possible in this way, while trying to avoid having to remove frozen bottles of water, which will thaw and have to be re-frozen later.

Although filling the empty space with blocks of polystyrene (polystyrol) will avoid the warm air problem, and reduce conduction of heat **into** frozen food, it will also reduce conduction of heat **out of** food which is not yet frozen. This increases the time it takes for food to freeze, which increases deterioration because the food is at a higher temperature for longer. The polystyrene will provide almost no "thermo-inertia".