> it's difficult to cool the whole house or even a single room by leaving the freezer door open

I think cooling with an open freezer is impossible in general? Or is that your point and I don't understand the argument?

The point is that just dumping an arbitrary amount of cold into the house is unlikely to change the temperature because the thermostat has access to more heat, and has a different goal.

That example was meant to illustrate why simple one off actions have a diminished or imperceptible effect on the system.

It's just not a great one because an open freezer or fridge will not cool a room at all, anyway: it pumps heat (with some inefficiency, i.e. more heat) from inside itself into the room, so it will on average heat up a room if it's left with its door open.