...so it can think really hard all the time and come up with lots of great, devious evil ideas?
Again, I wonder why no group of smart people with brilliant ideas has unilaterally imposed those ideas on the rest of humanity through sheer force of genius.
Look at any corporation or government to understand how a large group of humans can be driven to do specific things none of them individually want.
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.
An equivalent advance in autonomous robotics would solve the force projection issue, if that's what you're getting at.
I don't know if this will happen with any certainty, but the general idea of commoditising intelligence very much has the ability to tip the world order: every problem that can be tackled by throwing brainpower at it will be, and those advances will compound.
Also, the question you're posing did happen: it was called the Manhattan Project.