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.
The inference is more like "people place sufficient amounts of infrastructure under direct control of a sufficiently capable AI" -> "there is no way to ensure that humans will actually be able to shut down the AI". My claim is not that this inevitably means that the AI will resist shutdown, or that it will inevitably take harmful actions, just that there is a nonnegligible chance that it could. The downside is large enough that even a relatively small chance is something to be worried about.