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coming away from our victory, as a result of the perceived threat represented by the Soviets, we didn't demobilize our armed forces and in fact continued to keep troops stationed in places
Paul, we had a massive and chaotic demobilization of our armed forces after WWII. Headcount went from 12 million in June 1945 to 1.5 million in June 1947, and annual expenditures went from $90.9 billion in January 1945 to $10.3 billion in 1947.
By both choice and necessity, the Truman administration relied more on economic than military power to achieve its foreign policy aims. Strategic planning reflected this emphasis. The Joint Chiefs did not approve a statement of general military strategy until mid-1947, nor a war plan until 1948, for they accepted the State Department's assessment that the main danger facing the United States was political rather than military.
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Although the pace and scale of demobilization dismayed the President and his advisers, almost everyone agreed that major cuts in defense spending were in order. Administration officials perceived no immediate threat to U.S. security and feared that the continuation of wartime expenditures and deficits, or anything approaching them, would bankrupt the country.
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The cessation of hostilities would have prompted defense cutbacks in any case, but the fiscally conservative mood of the country, which Truman and his advisers shared, caused what in retrospect appears a precipitous dismantling of the American military machine.
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No pervasive, national security "ideology" characterized U.S. military thinking in the early postwar period. The disorganization, misconceptions, and infighting that had disrupted the military services during the war continued well into the postwar period. This does not mean that the military services did not engage in contingency planning for wars of the future, against Russia among other hypothetical enemies. Military planning, however, was not the same thing as actual defense programs, for the Truman administration did not believe that the Soviet Union posed a direct military threat to the United States at the end of the war. Instead, the containment doctrine that evolved from early confrontation with the Soviet Union would prescribe primary reliance upon the greatest American asset of all, its unrivalled economic power.
From Robert A. Pollard, Economic Security and the Origins of the Cold War, 1945-1950 (New York: Columbia University Press, 1985), pp. 20-23
http://tinyurl.com/3vydxk
Note that aside from just a factual correction, this probably means the phenom you're looking at ... standing armies ... might be of even more recent vintage than you claim, which probably strengthens your point rather than weakens it.