To put it simply, it could outcompete humanity on every metric that matters, especially given recent advancements in robotics.
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.
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.
“AGI” has proven to be today’s hot marketing stunt for when you need to raise another round of cash and your only viable product is optimism.
Flying cars were just around the corner in the 60s, too.
All of these entities would have been enormously more powerful with access to an AGI's immortality, sleeplessness, and ability to clone itself.
If Alexander could have left perfectly aligned copies of himself in every city he passed, he could have gotten much more control and authority, and still avoided a fight by agreeing to maintain the local power structure with himself as the new head of state.
The problem you're proposing could be solved via a high quality cellular network.
The Manhattan Project would be a cute example if the Los Alamos scientists had gone rogue and declared themselves emperors of mankind, but no, in fact the people in charge remained the people in charge - mostly not supergeniuses.