I want China and India and Africa to have first-world standards of living, with similar per-capita GDPs. That will be awesome, both for them as well as for the US and Europe.

Yes, standards of living is the big thing, and not just across china, india, and africa. I would be fine with the US's dominance if I though other people in the world could have satisfying lives where they don't have to worry about employment (and the resulting food, shelter, health care). But, we are probably decades from achieving that in even China and India, both of which have a lot to offer the world even now.

Unfortunately, the US also has many inherent resource advantages (pretty amazing farming, for instance), which much of the rest of the world doesn't have. I really don't see at least the arid parts of Africa competing any time soon on material goods, and they don't have the education or cultural draw to attract production of intellectual goods. So at some point, the world does need to help itself out. It's not just going to magically fix itself without people helping each other.

I guess I should make this clear: I'm not advocating some kind of world socialism thing. I'm pretty sure things like classes are inherent in human societies. But I would like to drastically reduce the difference between the poorest and the richest people, and I do want to make sure that the basic things we take for granted in the US are available everywhere.