The problem with invoking the broken window fallacy in reference to WWII is this: it implies that all military actions and wartime production was literally done only and solely for the purpose of creating jobs and producing something. That is, the war had no purpose in itself and was like the random destruction of a hooligan smashing windows motivated by the belief that his vandalism is justified just because people will be paid for fixing the broken windows.
The libertarians invoking the broken window fallacy here are guilty of the truly bizarre inability to accept that
(1) US war spending was done in order to defeat Nazi, Italian, and Japanese fascism, and defend the democratic world from tyranny, andThese facts do not entail that any Keynesian economist advocates war or natural disaster as a way of stimulating the economy.
(2) that war spending did indeed have the concomitant consequence that US income, employment and output increased, even if it was obviously not the type occurring in peacetime.
The absurd assumption of the libertarian critics is that the wartime economy must have been simply like a peacetime economy in all respects (something which I do not think any Keynesian has claimed), so that the discovery that it was not is then touted as some devastating argument against economic benefits that the US command economy did have. Amongst those benefits was that (1) private sector income was increased and this allowed a substantial reduction in the level of private sector debt (which had been a major drag on the economy since 1929), and (2) the accumulation of both personal and corporate savings during war that could be drawn down after the war ended.
Moreover, the assertion that all war employment did not contribute to private sector growth is unconvincing. First, there is the scientific and technological advancement that occurred via employment, spending and R&D related to the war, such as jet propulsion, new aeronautic technologies, radar technology, nuclear technology, surgical innovations, and so on. These technologies provided lucrative to private sector businesses and still are.
Secondly, many industries were created or strongly developed in new ways in the war years, and proved to be just as important after the war ended, such as the aeronautics, motor vehicle, pharmaceuticals and antibiotics industry. Many of capital goods created in the war years were also useful after the war ended, directly or with some adaptation.
The argument that wage and price controls distorted real GDP figures, while true, has little force given that (1) much of the production in the war was not for the private sector, but the government sector, and (2) that the private sector itself practices massive administration of prices even in peacetime, yet that does not stop people from buying what they want and shunning what they do not want.