The reason the economy prospered after -emphatically, not during nor because of- the war is that federal government outlays and taxes declined dramatically. In spite of millions of soldiers returning to the nation without jobs, the economy thrived.
War probably would benefit a few individuals/firms such as weapons dealers, air craft manufacturers et cetera.
Is war good for the economy? Thought experiment:
The United States is in a recession. Economic growth is declining and it needs to grow. So the government subsidizes a firm to build an entire fleet of aircraft carriers, rifles, ammo, explosives, uniforms, and aircraft. The carriers are sent into the middle of the Atlantic whereby all personnel are safely evacuated and the carriers are sunk. WIth all the economic calculation, labor input, engineering, production, savings, investment, planning, and so forth at the ocean floor, the Americans dance and cheer at the wealth and prosperity “created.”
All these inputs went into “goods” that were destroyed- what could have been produced if production structures weren’t diverted to war materials? Who knows. But market actors are poorer because of this diversion. It’s just a broken window.
Of course, this is what happens in war. War is a vice on economic growth. It may produce some transitory benefits for some individuals including jobs and higher incomes for certain firms and politicians involved, but it is at the expense of factors of production that are ultimately wasted as the products of these inputs are, literally, destroyed. Countless resources that could have been used to produce goods that consumers actually demand are instead directed to production processes that produce materials meant to be destroyed. Economic goods are misallocated and, as a user mentioned above, the Production Possibilities Frontier shifts left (declines; becomes poorer) as wealth is destroyed.
Pssst- Both Hazlitt and Woods talk about the effects that war has on an economy in those books!