Your points are excellent. I was just trying to make the point that if and when robots with AI become sentient, they may be much different than the homogeneous robots depicted in the terminator movies. If they truly become sentient, they may develop into distinct individuals, with varying personalities and psychological issues that could impact their functionality. Their ability to do quicker calculations, for example, does not guarantee that the totality of what they will be will be superior to human beings.
I'm no expert on evolution, but the mechanism which allows distinct human personalities is part of our ability to evolve. More successful combinations of traits would tend to survive. Less successful combinations would die out.
Robots could perhaps purposely implement a similar ability to vary their "personalities" so as to accidentally discover superior combinations. Future robots may need to pass a background check before being allowed to arm themselves. Some of them may just go nuts from time to time.
The sci-fi classic "The Day the Earth Stood Still" depicts an alien race which fully empowers their robots to keep the peace. Fun movie.