The world could do a lot worse than having us in charge. And we are in charge, make no mistake. As a country our we are doing writ large what Augustus did personally when he reorganized the Roman Republic and created, through sheer will alone at times, the Roman Empire.
Augustus knew that the remembrance of power which the senate had was something not soon forgotten. He also had the abject lesson of his great-uncle being pinata'ed just outside the senate building a few years before to instruct him on just what the senate as a group thought of people that tried to take away all their perqs.
But he also knew that this fractious bunch of old white guys couldn't govern themselves out of a paper sack any more. The Roman Republic was set up to run a city and a smallish state, where everyone pretty much knew everyone else, and everyone else's business. It was not set up to run the largest and most diverse empire the world had ever seen.
So he took the place over, but he did it carefully. No naked power grabs, or at least no real large ones, paying attention to, or at least pretending to pay attention to, the petty bullshit of the senate, making sure powerful people were happy and weak people were secure, and personally ensuring the army could keep the entire empire safe. Happy powerful people don't raise their own armies to oust you, and safe poor people don't riot and yank you out of the senate in pieces (this happened to rulers all over the world quite often in history. It was only the development of the machine gun in the 20th century that the mob ceased to be a very real threat to the governing classes). If it wasn't important, he let the senate handle it. If it was, he handled it himself and let the senate approve of his actions. Luckily for Rome, Augustus was one of those 5% of despots that actually have a clue, and Rome prospered.
Unluckily for Rome, Augustus made the common mistake of despots through history by assuming he was immortal. When he did finally keel over, at the ripe old age of 73, he left no real mechanisms in place for the transfer of power. This would prove to be one of the main reasons for the empire's eventual disintegration. It was bad for them, but good for us. We'd all probably still be speaking Latin if it weren't for this mistake.
The USA as a nation seems to be, so far, doing for the world what Augustus did for Rome. We didn't ask for it, and as a nation (the "people" part of the "we love the American people but hate the American government" saying) we don't much like it. But nobody else seems to be capable of doing the job, and now that nuclear weapons have been invented problems can get a lot worse than a bunch of butt-scratching barbarian tribesmen sacking a few cities.
Europe used to be, if not good, at least effective at ruling the world. But they were mostly interested in using the rest of the world to gather up enough cash to pay for the next war they felt like having for themselves. Think the middle east is chaotic? The machine gun, an American invention, nearly didn't make it until Hiram Maxim went to Europe, because he was told "Europeans will always pay top dollar for new ways to kill each other."
The only reason Europe is peaceful today is because they managed to drag the entire world into their little killing sprees not once but twice. The US and the Soviet Union got so damned sick of it the second time through they sat on them all for the next thirty five years (on the US side) before turning them loose. The Soviets never really got over it, which is understandable when you remember that roughly every tenth person killed in the war was a Soviet citizen. They only let go because they had to. This is the first time in about fifteen hundred years that the Europeans have played nice with each other, and probably the first time in history that they didn't have anyone else making them.
Japan made a stab at taking over the world at around the same time, or at least the part of it they were interested in (Asia, mostly China). It looked like it might actually work until the US, which was supplying the oil they needed to run their little war of conquest, cut off the taps. Someone over there, we're still not quite sure who because they burned all their papers before we took the place over, decided it was time to take those damned round-eyed gaijin out of the picture. It only took us four months to finish them off when we focused on them.
Both China and the Turks had a real good shot at running the world. China had invented paper, gunpowder, iron smelting, and a whole raft of other near-industrial items by that time, and sent a fleet over Europe's way to see why it had gone all quiet over there a thousand years ago (they really do think like this). But the fleet was recalled and then China just sort of ossified for the next few centuries. They're still recovering.
The Turks had taken over pretty much all of the old Islamic kingdoms by this point (we know them as the Ottoman Empire), and were literally knocking on Vienna's door. Due in no small part to one Vlad Dracula's efforts at slowing them down (having 25,000 prisoners impaled in a nice neat stadium pattern tends to unnerve even the most hardy of warriors), they weren't able to crack the place, and fell back. Again, for reasons not completely clear to anyone they never really seemed to recover from this setback. And so the people that were on the forefront of knowledge and culture when Europe was a bunch of scrabbling hicks seeing who could build the biggest dung pile ended up less than two centuries later prostrate before those same people. They're still recovering too.
And so the world is left with us. In spite of all the shirt-tearing and breast-beating done by the world's media, you all could do a helluva lot worse. Here in the US we're all so busy bickering with each other that we can only get it together for the really important stuff. Our government isn't any better than anyone else's when it comes to dealing with the outside world, but savvy people at least can get the media to expose the worst of our excesses. Transfer of power is built into our government, giving the truly dangerous and incompetent a chance to both grasp power and have it destroy them in a short enough time not to break anything important.
And, at the core, we are you. America, time and again, takes both the best and the worst the world has to offer. Be repulsed by us, but realize that we learned to be repulsive from you. Be inspired by us, and take heart in the fact that what is inspiring in us comes from you. Be angry at us, even afraid of us, but always realize what angers and scares you is only what you brought or gave to us.
And always remember that, no matter what we're like right now, the one thing that is always remarkable is that we change. Don't like us now? Wait. Learn. Work with us to change us. We're running a planet with no instructions. We need all the help we can get.