However this goes, this seems to be a huge argument in favor of big-government spending (if we get this much utility from the government building things that literally explode themselves without providing non-military utility, then in a time of peace, we should be able to get even more by having the government build things like high-tech infrastructure, places of beauty, peaceful scientific research, large-scale engineering projects, etc.). So should we be spending 20-40% of our GDP on peace-time government mega-projects? It's either that or this piece of common knowledge is wrong (and we all know how reliable common knowledge is!).

I'm surprised no one has explained this yet, but this is wrong according to standard economic theory as I understand it.

1. The United States suffered from terrible monetary policy during the Great Depression.
2. Due to "animal spirits" and "sticky wages" this caused large scale unemployment and output well below our production possibilities frontier.
3. World War II caused the government to kickstart production for the war effort.
4. Living standards actually didn't rise, although GDP did (GDP per capita is NOT the same as living standards). Consumption was dramatically deferred during the war. People had fewer babies, bought fewer consumer products (and fewer were produced) and shifted toward home production for some necessities.
5. There was a short recession as the end of the war lowered demand, but pent-up consumer demand quickly re-stabilized the economy.

The point is WWII helped the economy because we were well under our production possibilities frontier during the depression. Peace-time mega projects would only be helpful under recessed/depressed conditions, and fortunately, we now can use monetary policy to produce similar effects.

Anyway, the argument you were making seems pretty common among people who don't follow economics debates, and in fact is one of the major policy recommendations of the oddball Lyndon LaRouche cult.