Step 1: AI earns money
Step 2: AI pays people to kill each other

That is probably sufficient, but AIs also have deception, blackmail, threats against family, direct action, and other tools at their disposal.

And I agree with the Count – AI doesn’t have to decide humanity should be destroyed; it just has to decide to make number go up.

These were actually a thing. Search for “shockers” here:

https://penny-arcade.info/the-strange-the-unusual

(Note: not Penny Arcade the comic; aren’t domain names fun?)