It’s not about motivation, it’s about doing whatever it’s been programmed to do, and grabbing whatever means it can to that end. Now something as puny as a large language model won’t have much reach (the current ones can’t even read the internet after the initial learning phase), but if you have a way to give the thing an unbounded goal, then it will use all means at its disposal to make that goal happen.

Heck, even if you just give it some hard maths problem, the machine might think of ways to turn the entire solar system into a giant computer, using us for spare parts along the way. That requires a sufficiently accurate model of the universe of course, as well as ways to harness that model (say the AI starts by convincing humans to build robots and factories — which would be quite easy if it’s good at playing the stock market game).