Modern Superman is pretty explicit that Supes doesn't really have loyalty to the US Government, he just believes in "the American Way", ie liberal freedoms. There's one story in particular where Superman rescues a North Korean submarine from sinking, and Americans get pissed off at him, so he has to try and explain that he values all human lives and doesn't put stock in who the government's current enemies are. If I did a Superman in the USSR story, it would be like that - Superman is raised as a socialist and believes in the international project, but while he would defend the USSR from capitalist aggression he wouldn't let himself be used as a "weapon" by it.