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The goal is to have the fire drive a high airflow, both to give itself oxygen, and to pass the exhaust through a long path of heat absorbing dirt. The metal drum does this by passing the hot exhaust up through its center, then rapidly cooling it as it falls back down along the metal surface. The difference in density drives the airflow. The drum needs a high thermal conductivity to be able to maintain this temperature and density difference, and this is also the primary way the heat is transferred to the living area. The earthen part gathers up the remaining heat to increase efficiency and retain heat for when the stove is off, but most of the heating is done immediately through the metal.
The heat is all being dumped into the living space either way, so you aren’t losing anything from the metal. It takes away from how much heat will be available in the earthen part after the stove is turned off, but it still warms the room. Plus I imagine it’s nice to have some heat immediately instead of having to start the fire hours before you actually want it.
You could adjust the design if you wanted to change the ratio of fast heat and slow heat, but you would always need to have some part with a high thermal conductivity.