That's not really true, for instance Singapore isn't really democratic (it's effectively a one-party semi-totalitarian 'democracy') and you know what, it works really well there.
Singapore has also really only existed in its current form for a bit more than a half century and has had three leaders, two of which were immediate family. It hasn't really shown that autocracy works over longer time scales - in history there are plenty of cases where benevolent autocratic governments (monarchies, empires, etc) had extended periods of stability and prosperity.