For the longest time, we've been under a hegemony that was originally far more stable than the world before it. This has helped to bring an unprecedented era of prosperity. The American empire is perhaps the first empire in history where people want to be under its banner as opposed to out in the cold.† But current antics threaten that very tenuous stability that was fought over for so many centuries. It is not without any faults, but out of all the alternatives out there - this is the most peaceful one.
Yes, there are arguments that broadening the base of support will help not hinder stability.ß The fact remains that this is the best system we have found so far and it does actually work. We might even someday have something far more stable than this, but the transition to that is not going to be easy. In fact, I think that on the existential risks meter of the world - stabilising American hegemony should be a priority. It is vital that this system is maintained until a better one emerges to take its place.
People might disagree, but it really is a tragedy that countries and groups now want to overthrow the American hegemony largely due to political missteps at home and a steady disconnect between what it means to be hegemon and the day-to-day of American politics. They've forgotten that their alliances were built upon shaky ground and need upkeep to maintain. And that even the firmest of empires do fall.
† http://www.middlebury.edu/media/view/214721/original/OdomPap... ß http://www.economist.com/blogs/democracyinamerica/2012/02/wo...