No, they are legally obligated to destroy the world. The greatest system humans have ever devised.

Always wondered what Skynet would have done had it killed off the humans in the Terminator future. Would it build a machine society?

There are some acceelerationists who want "superior" machines to replace humanity. But what if instead they get the equivalent of a paper clipping gray goo, or a bored Skynet who just fights it's own creations? Is that worth replacing all the humans?

As a thought experiment, what is a p doom AI doing after humanity is gone?