Friedman is mostly worthless too. Mises and Hayek, along with their successors (Rothbard, Kirzner, Block, Hoppe, Hazlitt, et all) are the only ones who can coherently explain the business cycle in the first place. The Keynesian school, Chicago school, monetarists, socialists, and all the other schools of economic thought besides the Austrians have no way to explain why we have a constant boom and bust cycle which is why they never see the busts coming.
But anybody who thinks war ended the Depression is wrong. Sorry. It shows a fundamental lack of understanding of basic economic principles and logic.
Of course GDP is going to go up if you calculate it using a formula that assumes government spending has the same effect on prosperity as private spending does, then massively increase government spending.
That's why it's a popular misconception. Because a lot of people believe it. But it makes zero logical sense.
If you spend shitload of money making tanks those resources cannot be repurposed easily into anything that benefits the average person. It doesn't make him more wealthy, it makes him less so. Not only is there less money to spend because so much has been spent on weapons, but there are also less material reources with which to make new goods or provide new services.