The US were much more mechanized then any other army in the war, though I don't think it was cultural. It was much to do with their industrial capacity. IE if the other countries in the war could have put out as many motorized vehicles as the US, they would have, but what industrial capacity they had was going towards more objectively important weapons (planes, tanks, artillery).
For instance, almost all the cars used by the soviets were manufactured in the US. It helps that the US had the largest car industry going into the war. The only other country that could match them in this respect was Germany, and most of their car industry was diverted into tank production.
Motorized brigades would have made up a minority of every other army, the average soldier had to make do with marching, or if they were lucky, rail.
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