Plenty of American films had Soviet or Soviet-linked villains, but the opposite was not true. Here is one excerpt from:
The Soviet and American mainstreams expressed themselves in radically different ways, with different fears. Being a single party state, the Soviet Union was always factionalist and unsustainable, and could only perpetuate itself through cycles of repression and repudiation. Its anxieties were mostly directed toward itself; as the Americans made fantasies of threat, the USSR made fantasies of stability and global standing. The Soviet Union was also dominated by Russian culture, and inherited its taste for oblique metaphor and indirect address. (It should be noted that the three greatest filmmakers to come out of the Soviet Union—Sergei Eisenstein, Andrei Tarkovsky, and Aleksei German—never completed a film set in the present day.)
Simply put, it wasn’t an environment that was primed to depict the Cold War directly. But it was also an environment with a Cold War mythos that was very different from that of the West. The Soviets did have a “worthy villain,” whom they beat year after year on the big screen: the Nazis. The Soviet Union was the hero who slew the dragon; defeating the Third Reich was a point of national pride. There would never be a more important opponent. The Soviets couldn’t reasonably elevate the Americans to the same status, or even to the status of the White Guard of the bloody Russian Civil War—the USSR’s origin-story villains, in a way.
…Americans couldn’t be expected to kill or die for their cause, because—as the 1965 spy film Game With No Rules, set in Berlin at the start of the Cold War, suggests—they didn’t have a cause to begin with. Instead, the rare American antagonists of popular Soviet film were portrayed as pawns of business interests, military-industrial collusion, or, of course, the Nazis. Portraying a monolithic United States of true believers, focused on the eradication of the USSR, would have gone against two essential aspects of the mythology of Soviet propaganda: the defeat of Nazism, which rid the world of an evil the likes of which it would never see, and the notion of communism as a self-evident ideal.
For decades, Soviet media attacked the United States—with varying degrees of subtlety—as a broken society, its failure obvious. Capitalism and Western democracy weren’t values that could inspire the same kind of commitment as communism, and the only reason anyone would fight for them was because they’d didn’t know better.
Here is the full piece, via someone in my Twitter feed sorry I can no longer find it.