The Kingdom of Bhutan is a fully functioning monarchy, and in spite of that ranks very high in what it calls "Gross National Happiness." To be sure, it is a benign dictatorship, one in which the monarch makes quite a show of being concerned for his subjects. Historically, this paternalistic approach to governance has actually been the norm. It wasn't always as good as hoped for, but most rulers desired to see the needs of their people be well met.
Additionally, Isaac Asimov once postulated a United States in which the "best" person was selected by a computer to be President, after neutrally testing any applicants who desired to run. The crux of the story was that in one year's cycle, the computer refused to pick anyone, because no one was fully up to the task. There is nothing that says that people necessarily choose the "best" person for the job. Indeed, being too much of a policy wonk may help the government run better, but still fail to capture the people's love. Mario Monti, Prime Minister of Italy, is often called a "technocrat," and widely heralded by pundits as a result, but is almost certain to be defeated in the next election. A match-up against his predecessor, Silvio Berlusconi, held in any kind of public forum, would have been a massacre. But when bond yields plummeted, Monti made good.
Indeed, it is real work to be an active participant in one's own governance, and so one could argue that if happiness (utility in economic terms) were the only desired outcome, then a despot attuned to the needs and wants of his people is actually a better system.
Unfortunately, as Madison said, "if men were angels, we wouldn't need government in the first place." As such, such benign dictatorships, while definitely the model of Plato, are rare in practice. And thus, pragmatically, representative democracy's advantage of incentivizing the goal of looking after the people by giving it power as a reward tends to eventually win out. In the word of Winston Churchill, "Democracy is the worst form of government, except for all the others."