The Austrian free market explanation as I understand it is that most of the WWII economic controls were relaxed or eliminated in 1946-7, not as part of some grand free market strategy, but just sort of de facto. Spending was massively cut compared to what it was during WWII, and even many of the most onerous New Deal policies were relaxed or eliminated around that time, if they hadn’t been already.
If you look at this graph of US federal spending as a percentage of the nation’s GDP (a pretty good yardstick of the size of the gov’t’s footprint relative to the rest of the economy), you’ll see that while WWII led to the largest gov’t footprint relative to the nation’s economy, there also was the single biggest drop in that footprint in the immediate aftermath of the war.
https://www.researchgate.net/figure/US-Government-Spending-as-Percent-of-GDP-Government-Spending-in-US-from-FY-1903-to-FY_fig1_227415421
(of course, you’ll also notice that today’s “normal” is a federal gov’t ALMOST as big proportionally to the US economy as during the peak of WWII wartime economic fascism, which is a disquieting realization.)