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There were a ton of policies enacted leading up to and during WW2 that restricted free enterprise, and I'm using "tax rates" as sort of a catch all here. This is an interesting article about it:

In 1944, government spending at all levels accounted for 55 percent of gross domestic product (GDP). By 1947, government spending had dropped 75 percent in real terms, or from 55 percent of GDP to just over 16 percent of GDP. Over roughly the same period, federal tax revenues fell by only around 11 percent. Yet this “destimulation” did not result in a collapse of consumption spending or private investment. Real consumption rose by 22 percent between 1944 and 1947, and spending on durable goods more than doubled in real terms. Gross private investment rose by 223 percent in real terms, with a whopping six-fold real increase in residential- housing expenditures.

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On paper, measured GDP did drop after the war: It was 13 percent lower in 1947 than in 1944. But this was a GDP accounting quirk, not an indication of a stalled private economy or of economic hardship. A prewar appliance factory converted to munitions production, when sold to the government for $10 million in 1944, added $10 million to measured GDP. The same factory converted back to civilian production might make a million toasters in 1947 that sold for $8 million—adding only $8 million to GDP. Americans surely saw the necessity for making bombs in 1944, but just as surely are better off when those resources are used to make toasters.

How did that sudden shift happen?

When the war ended, however, the command economy was dismantled. By the end of 1946, direct government allocation of resources—by edict, price controls, and rationing schemes—was essentially eliminated. Tax rates were cut as well, although they remained high by contemporary standards. By any measure, the economy became less subject to government direction.

And in the conclusion:

Central to this, however, is one important factor: The price mechanism must be free to efficiently direct resources to their best valued uses. This, in turn, implies that regulations that impede this market process must be eliminated as government spending declines. Ironically, it seems that the postwar prosperity that America enjoyed after World War II was less the result of a carefully crafted political agenda than a by-product of what government stopped doing.

Basically, the government stopped directing the economy (i.e. taking taxes and spending as it saw fit) and allowed the market to dictate how money would flow. The result was a (relatively) smooth transition to a peacetime economy, which was capable of taking advantage of ravaged economies elsewhere in the world.

Not slashing taxes… taxes were at their highest in the 60s.

That's irrelevant. What matters is the relative change and the signal that sends to the market. Top tax rates were 94%, and dropped substantially (to around 86%-ish top marginal rate, corporate taxes also cut) after the war. But then we had the Korean war, and taxes increased again. But again, it's the signal that matters here, not the absolute numbers.

There are a ton of other factors. My general thrust is that there was a huge drop in government spending and therefore a lower need for revenue, and that opened up that money to be used for other purposes.