As much as I share the overall reading of XX century Italian history you propose, it does not support a causal theory between the Constitution and what followed. The Italian Communist Party was one of three dominant forces shaping the Constitution (the other two being Socialists and Christian-Democrats); they were as interested in avoiding centralization as anyone else, in order to keep Fascist nostalgia at bay. Most Communists in the Assembly had been freedom fighters, some of them for decades, at huge personal cost; their priority was to avoid a new Mussolini ever appearing.

Once the Constitution was in place, overall political debate was indeed shaped by Cold War events and influences; but the document itself is arguably a pinnacle achievement of political theory, pushing representative democracy and collective responsibility to their limits.