[As soon as the stove heats and any water rises from the stove, it has to be replaced with cooled water descending to the stove. So you need the heat dump/cylinder above the stove.
The heat dump is all those parts of the circuit not providing the heat.
Water will ascend from the stove. It starts cooling straight away, and gets to the top having been pushed by more water from below. This is not magic, the stove is supplying the power. Meanwhile water will be drawn up from below the stove (or it is being pushed by the water ascending from the stove and thus bearing on the water in the rest of the circuit).
It is a cycle, that's the way it works, the water goes around and around.
Can't argue with that.
Your theory has the water ascending from the stove, replaced with water ascending from the cylinder below. Do you wind up with all the water in the attic? The water in the stove will boil.
Ah! but the water at the top of the circuit continues round the circuit, descending to the cylinder below.
Water in solid fuel systems often boils, even where the stove is below the cylinder.
It won't work. The end.
It is a cycle, that's the way it works, the water goes around and around. Hmmm......haven't I seen that somewhere before?