Is the most likely doom scenario of an AI apocalypse another version of the very hungry caterpillar story, where instead of having an insatiable amount of hunger for food, it's knowledge?

So that at the end of the doom scenario, the whole world turns into a giant computer just so the AI can solve a difficult puzzle?

The most likely doom scenario I’d reckon is a global food crisis from climate change, resulting from trying to build out the data centers needed to adequately power the infrastructure necessary to keep expanding the corporate AI build-out.