Peace is not merely the absence of war. Peace grows from public order. Just as a city with no public order is a city at war with itself, world peace can only come through world order. Rogue individuals can destroy the peace of a city through their disordered behavior; this is why order is enforced by "peace officers" (police, sherriffs, etc.) Rogue states pose the same threat to the peace of the world as criminal gangs to to a city; therefore, a global "peace force" is needed to maintain the order necessary for peace to exist.
The only question is who will enforce order -- and by what code will they judge lawbreakers? I submit to you that the United Nations is neither suited for nor capable of playing this role in the world; the opportunties for abuse within a body as fraught with conflict and competing third-world agendas as the UN are simply too great, and the UN Charter is too thinly-worded to be a secure guarantor of individual human rights. The posession of unlimted power coupled with a lack of codified human rights would soon turn the UN from a global cop into a global prison guard. Therefore, it is left to private actors -- nation-states -- to serve as the global cops.
I submit to you that the United States, with its Constitution, traditions, and military supremacy, is (with its like-minded allies) the only nation that can hope to serve as an enforcer of peace on a global scale.
Some cry for a republic, not an empire. That is a cry that all Americans would gladly take up, if possible. But in a world where rogue states, non-state terrorist actors, and crime syndicates can wield the frightening power of the atom, the option of retreating behing our pelagian shields and existing in serene aloofness is one no longer open to us. If we wish peace -- a peace based in global order -- then it is up to us to provide that order. If our choices are global chaos or pax americana, one may forgive one's preference for the latter.