You’re still skipping step 2. “People automate lots of infrastructure” -> “the AI is now an autonomous, self-preserving organism that humans can’t shut down” is doing an enormous amount of work here.
Why does it develop a shutdown-avoidance goal? Why can’t its operators revoke access? How does it manufacture replacement hardware? How does it acquire energy, chips, robots, raw materials, etc. against human opposition? How does it defeat other AIs controlled by humans?
“Eventually we give it enough control” isn’t an explanation of those things. It’s just assuming the conclusion.
Don’t get me wrong I think there are real AI dangers. Like AI powered war drones, mass surveillance, economic destabilization as jobs disappear and our system has no way to make sure everyone shares in the economic gains.