Superman by his creators Jerry Siegel and Joe Shuster was very patriotic, assisted the U.S. Army, gave obedient service to U.S. service men. He took the U.S. side completely.
Superman assisted the U.S. in fighting Nazis and the Imperial Japanese military. Superman is shown sinking battle ships, destroying planes, destroying tanks, etc. Ordinarily of course Superman wouldn't kill enemies. Killing in war is justified by law. He doesn't like it of course but he can't really save and in-prison all of the enemy solders. There's far too many of them. Although he does end up working for the state, he is also working for the people of the state and the preservation of the free world, not just the entity of the U.S. government. He's doing violent deeds in our defense. He's trying to protect the free world, and the American Way, the Constitution of the United States to preserve freedom, life, liberty and the pursuit of happiness from those who threaten our freedom.
And in the Fleischer Superman cartoons based on these Superman comics he assisted the U.S. in fighting Nazis and the Imperial Japanese military.
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Superman assisting the U.S. in fighting the Cold War Soviet Union military in the Dark Knight Returns was clearly influenced by all of this.
At the end of Dark Knight Returns Frank Miller writes:
With Acknowledgment to the works of
Dave Fleischer
Max Fleischer
Joe Shuster
Jerry Siegel
And Frank Miller's idea that these superheroes would be vilified by parents groups, the media, and be called in for questioning by a Senate Sub-Committee was modeled after the real-life vilifying of these characters and the U.S. government proceedings against them in the 1950s. In reality these superheroes Batman, Superman and Wonder Woman were vilified by parents groups, the media, a psychologist named Frederick Wertham and a Senate Sub-Committee on Juvenile Delinquency called the comic book publishers in for questioning and they eventually make a pact with the government that they would give them their obedience or disappear. It happened in 1954 and the original strict Comics Code was created, those that weren't code approved were forced out of publication because the threat of newsdealer boycotts were pressuring them into not selling what somebody had found offensive. DC editors had been censoring Batman comics since 1941 when they created an Editorial Advisory Board so by the 1950s it was actually the horror and crime comics Crime Suspenstories, Crime Does Not Pay, Tales of the Crypt, Vault of Fear, Haunt of Fear, that made comics all look like monsters and really soiled them in the public eye. Batman is at his core a horror-esque character dressing as a bat to frighten and had very brutal methods before DC editors censored the character, so Frank Miller puts Batman in the role that the horror and crime comics and their publisher Bill Gaines were in at the time that these things really happened.