From the graphic novel:
"Nobody can make you do anything you don't want to do, Clark"
"These aren't the old days, Bruce... World's got no room for...
The rest of us learned to cope. The rest of us recognized the danger--the endless envy of those not blessed. Diana went back to her people. Hal went to the stars. And I have walked the razor's edge for so long.
They'll kill us if they can, Bruce. Every year they grow smaller. Every year they hate us more. We must not remind them that giants walk the earth.
The Dark Knight Returns is basically a postmodernist deconstruction of the superhero genre. It shows a world in which superpowers don't make you a hero, they make you something that normal people fear and hate. Superman has decided that the only way to avoid that and still help people is to become a complete subordinate of the already most powerful government and restrict his own decisions to permissible interpretations of his orders.
Acting independantly would turn people against him - like Batman. Supporting any other government or organization would make him even more of a pawn in global power struggles. At least the US government is unlikely to order him to do something truly horrible out of desparation.