ASI (Artificial Super Intelligence) would never go the route of clumsy slaughterbots. It might create a famine or release a 99% fatal Covid.... but Terminators? That would simply be silly.
On “Judgement Day” the machine will find the human race guilty and the wiping out of the species will begin. Extermination of humans using the tools it has nukes, bio, chemical etc. Terminators are just a tool to explain in the movies the intent of “Skynet” for the future of the human race.
I always thought you were a pretty smart and intuitive guy. I am sorry that you don’t see the allegory in the story.
Imagine the machine digesting millions of hours of FPS games and watching how man treats each other. Thousands of hours of war footage.