I don’t believe the control problem is solved, but I’m not sure it would matter if it is.
I don't even understand what the proposed mechanism for "rouge AI enslaves humanity" is. It's scifi (and not hard scifi) as far as I can see.
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.
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.