Newt Gingrich was on Charlie Rose last night, and he reiterated a statement I'd heard most often in connection to the Project for the New American Century - the United States of America, as the strongest nation on earth, as the sole superpower, Must, absolutely Must, ensure its position, for the benefit of the United States and for the benefit of the world.
This statement seems to me to be born out of two beliefs - a moral imperative to protect/guide/lead the world, and a fear that a lack of strong global leadership from the US of A will lead to some other nation taking over global hegemony, which would invariably be a bad thing for the US. "We must be the superpower, because if we aren't, it will be bad for us."
This fear of other nations becoming dominant has lead to centuries upon millennia of nations striving to become the most powerful, to ensure their own survival, and then exercising power over other nations, to continue to ensure their own survival. Superpowers have risen, clashed, and fallen so that a nation's freedom/independence/autonomy etc, can be protected. Pax Romana, Pax Britannica, and Pax Americana all serve for the security of the titular nation, and exists not as periods without war, but without threats to survival. These, quote "eras of peace", have all hinged on the nation providing the peace doing well, and have all ended when the nations' power began to weaken. The stability provided by global superpowers is always a temporary proposition.
The hegemony that could benefit the world therefore cannot hinge upon the success of one nation. It simply cannot. Nations get overambitious, overextended, weaken, and then fall, and that cycle has very little stability relative to turmoil. For a global hegemon to be effective, it must be able to last beyond the lifespans of empires, and must be removed from the process the elevates and then breaks nations. The global hegemon must, therefore, be either extra-national or multinational, and must be able to ensure stability in spite of nations failing.
This'll be expanded on latter, but the global hegemon we need is a powerful United Nations, which avoids the pitfalls of a peace ensured by a given nation, and isn't nearly as easy to use to exploit the world as a single nation is. The other option for the US, instead of playing the part of hegemony until challenged or usurped, is to transfer the power to the UN, who simply cannot fall to a given nation.