You talking about the metal drum? Seems like that's necessary. He explains why in the video, tldw: it radiates heat which cools the exhaust, causing it to sink, and this starts pulling air through the combustion chamber. He calls it an air siphon at one point. Yeah you lose some heat from this, but without that siphon it won't create the jet furnace in the firebox. Maybe there's a way to engineer that without metal, I have no idea.
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.
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.
Metal has better thermal conduction (transferring heat from one end to the other) the brick/clay/mud is there for thermal insulation to trap more heat and keep the metal conducting even after the fire has gone out
so the rationale is that it warms up the whole thing faster? but that's at the cost of insulation & materials requirements. someone should compare a full brick version to this
It's not really a matter of heating it up faster, tho I guess it would, it's more about fuel efficiency i.e. how long the heating can last on the same amount of fuel
With the clay acting as an insulator, heat that would usually escape from a naked metal pipe would be retained and used to keep the metal conducting heat for a longer period of time (so more bang for your buck in terms of fuel)
I suppose you could use clay piping, but I doubt it could match aluminum piping in thermal conduction, it would require several experiments using different materials both metal and ceramic to find the sweet spot
the whole thing kind works on old principles so i was thinking how antecedents would work without high quality steel. involving ceramic is probably correct