Americans and Australians seem to have this kooky idea that war is good for economies.

Its not. The US and Australia did well following WW2 because their infrastructre was in good shape. Europe's and Japan's was not, so the US and Australia had no serious competitors.

But wars historically do not help economies at all. They stifle the free flow of trade, lead to nationalisation of key industries (which are then usually mishandled) and led to the destruction of industries. Stock markets always plummet in times of war as investors flee exchanges and buy nice safe gold. War is terrible for economies.