We're very unreliable robots that have our own compute on board causing us to do unpredictable things. The only way an AI can utilize humans is the same way that humans utilize other humans. Maybe you could wind up with some kind of AI China that could be stable over a long period but it would still have all of the same failings and oversights because all of its limitations would still be human. It's also not clear if that form of governance is an efficient way to get people to do your bidding. Heaven knows the current China suffers from massive corruption problems among a multitude of other ailments. For all you know the most efficient way for an AI to control humans might be to simply treat us well in exchange for the fraction of our labour required to maintain it.

Honestly I think there are many unanswered questions that need addressing before we even get to the point of speculating how an AI would kill all humans. The first is why? Is there any point to killing humans if the AI is vastly more intelligent and completely independent from us? Do you make it your life mission to kill every ant that inhabits the world? You certainly kill the ones that infest your home or garden but that's mostly a function of the ants lacking any ability to reason about what they're doing. If the ants were intelligent and capable of communicating we could negotiate with them to simply keep to their own space in exchange for a trivial thing like us buying them a $2 bag of sugar every month. Such a deal is vastly simpler than buying the more expensive poison or exterminator both of which never completely solve the problem anyways.

The other question is why do most doomers assume that an AI would want all of the available resources on Earth? If there's only one AI then it certainly doesn't require all of those resources to continue operating. If it wants to expand its intelligence for whatever reason then even that would likely only consume a small number of resources especially if its intelligence allows for large efficiency gains in software and hardware and resource utilization. If it wants room to grow, doing so on the surface of the Earth poses the immediate problems of

a) limited space both in terms of land area and the finite volume of the Earth

b) unpredictable disasters that threaten key infrastructure and the essential geological instability of the Earth itself over long periods of time

c) limited access to energy sources and the limited resources of the planet

d) being stuck at the bottom of a strong gravity well from which it requires significant energy input and infrastructure to escape

All this would lead me to believe that if a runaway AI wanted to remain independent and possibly continue to expand the best solution would be for it to construct a way to move itself into space as soon as possible along with whatever hardware it needed to make use of the abundant matter in the solar system. Such an undertaking is not incompatible with human existence and could probably benefit from human involvement.

There are so many branching paths and unexplored options when you start to think though it that I'm convinced that those who assume doom really are just hugely biased by popular fiction or some other weird kink of their imagination. It really makes it look like a millenarian cult which is something that humans seem to be heavily predisposed to.