Fair enough. Superman can't change human nature. But he can do more than than saving people. If he truly wanted to help humanity he would need to. If he's going to save people in Mexico being murdered by cartels, he is eventually going to need to address the issue of organized crime controlling the entire country. If Superman wants to save sex slaves he eventually is going to have to bring down those that control that business.
He needs to address the issues that the world's faces beyond just dealing with "the symptoms" that is the immediate victims can save. And I think that in order for that to happen he needs to go beyond "giving speeches". A lot of the times though is not that people lack inspiration it's that people in power simply don't benefit from helping everyone so they don't.
Yes, that's something that I think is interesting. Superman is an alien. He is god-like. He would completely transform the way people think about the nature of reality.
Superman has an obligation because he makes it his obligation. Just like Batman makes it his obligation to help Gotham. What he does is based on his character. Based on that I doubt he would just stay hidden in his fortress or take the passive role of trying to inspire people. His morals/values/relationship to the world are his obligation. His character is his obligation.