Are you sure that the the world's relatively peaceful period is due to the US military's hegemony? From where I'm standing, the US has been in a state of constant war for at least a decade.
Not only is it constant war, but it's a consumer war. Here in America, we are force fed this "Defend Freedom" rhetoric, while ignoring the people who live on this land who are in desperate need of some Freedom. Americans need to free themselves from the complex that has kept us invested in conflicts across the globe. I know we see ourselves as the "global-police", but it's time to take our priorities back to our people. I support the troops who do "defend our freedom", but I'll be fucked if going to war again means we are denied basic human rights here at home because we don't have the money.
Not sure. USA has been almost constantly at war since its inception. Many of the wars were for exploitation of native population and resources or outright conquest. But there have also been wars, especially recently, where the USA has been acting as the military might to enforce international law. It's usually in the USA's interest to maintain international peace, especially in economies that are open to globalization. But counterexamples abound... What other factors might have resulted in the current era of relative peace? Luck?