[Rain Man]

It seems like Superman could dart around and listen to everyone's negotiations and use his x-ray vision to read their secret documents, and then figure out if a solution exists that is workable for everyone. If not, then he can point out where the irreconcilable differences lie and then listen to a debate about which side should win. Then he can enact regime change to the other side until he gets a regime that will resolve those differences.

But it points out the fundamental flaw with a Superman-run world. Superman has no need for democracy, and relying on Superman to resolve world problems is essentially a one-world government with a dictator. Maybe he's a benevolent dictator, but he's still a dictator. Even if Superman can indeed solve the world's problems, he would do so at the cost of our self-rule.