Quite a few have succeeded in conquering large fractions of the Earth's population: Napoleon, Hitler, Genghis Khan, the Roman emperors, Alexander the Great, Mao Zedong. America and Britain as systems did so for long periods of time.
All of these entities would have been enormously more powerful with access to an AGI's immortality, sleeplessness, and ability to clone itself.
And of course the more society is wired up and controlled by computer systems, the more the AGI could directly manage it.
I can see what you're trying to say, but I cannot for the life of me figure out how an AGI would have helped Alexander the Great.