So, war (which--to reiterate--I am not advocating) would necessarily cause the American economy to "shrink dramatically"--so much so, in fact, that its currency would become essentially worthless?
I do not believe this happened as a result of WWII. Or as a result of WWI, prior to that. Or as a result of any other war in which the US has participated...
The revolutionary war was highly inflationary as the “continental” became nearly worthless. Confederate currency became worthless during the civil war. WWII was highly inflationary. Vietnam war was also highly inflationary.
Money is a piece of paper that entitles the bearer to some piece of the economy. During war, the non military economy shrinks. So unless you want to buy a tank or a fighter jet, there is more money around and less to buy.