Small boats used systems like this: freezing blocks of ice to provide convective cooling to a cooler so that things stay cold without the engine running.

A lot of people hated them enough (and the gas used while sailing) to replace it with solar based systems.

Regular refrigerators use the same principle, albeit with a mechanism much simpler than a heat pump. They have holes between the freezer and refrigerator compartments and use a fan to push cold air from the freezer to the refrigerator. A heat pump would make that exchange much more efficient.

I doubt that heat pumps could be more efficient than direct exchange of cold air?

There are periods where you don't want the cold air to move into the refrigerator. Direct exchange allows the cold air to move around at all times -- regular refrigerators just turn a fan on and off, but some heat is always exchanged through the holes. A heat pump would just make the exchange more controllable.

I have a fridge that works with just holes. You can either have the fridge or the freezer at the right temp but not both.