First we need to address the basic premise that could allow this to make sense at all in some house or environment -- that one can afford to freeze less during the day if they freeze it more at night (or vice versa).

For a fridge this is hard because you're usually targeting a narrow temperature band (don't want to accidentally freeze your veggies), but for a freezer it usually doesn't matter if you get it 10-20 degrees too hot or too cold as long as everything remains frozen. In that case, your losses (whether they're through the insulation or an open lid) will be higher with a colder freezer, so even if you could get your freezer down to e.g. -200 it might not be cost advantageous to do so, but colder temperatures definitely buy you some extra time. E.g. if normally your freezer is at -5 and you instead cool it down to -10, there will be a nonzero amount of time before it heats back up to -5 again (and the amount of time can be large if your freezer is well insulated and has a high thermal mass).

The "closed system" aspect of this is also interesting.

The cheap answer is that not all houses are heated or cooled (mine isn't), so you can sometimes ignore that part of the equation.

A better answer is that everything mostly works out the same even for closed systems. Suppose you have A/C that cools your home to a target temperature. When your freezer is running it moves heat into the living space, which then needs to be moved outside. As a system, you can pretend those two units are working together to move that same quantity of heat outside, and when the freezer is off you're just not operating that entire heat pumping system (assuming linear power demands and a host of other things to make the example tractable in a comment). While the freezer is off it will also assist in cooling the room down, further alleviating A/C power demands during peak hours (not alleviating them much, but helping nonetheless).

If you're instead heating the room to a target temperature, everything works a bit in reverse. The freezer alleviates heating costs while it's running and exacerbates them while it's off (and critically, it exacerbates them more than if you assumed a constant, low power draw because we're intentionally decreasing it's temperature below a typical freezer level and thus increasing the rate at which heat will enter it from the apartment by some small amount). Assuming you were trying to run the freezer during low cost hours, that effect might be large enough to offset any gains. I doubt it, but that's just a hunch, and I haven't run any hard numbers yet.