an AI will not have a fanatical goal of taking over the world unless it is programmed to do this.

It is true that an AI could end up going “insane” and trying to take over the world, but the same thing happens with human beings

Are you asserting that all the historic conquerors and emperors who've taken over the world were insane? Is it physically impossible to for an agent to rationally plan to take over the world, as an intermediate step toward some other, intrinsic goal?

there is no reason that humans and AIs could not work together to make sure this does not happen

If the intelligence difference between the smartest AI and other AIs and humans remains similar to the intelligence difference between an IQ 180 human and an IQ 80 human, Robin Hanson's malthusian hellworld is our primary worry, not UFAI. A strong singleton taking over the world is only a concern if a strong singleton is possible.

If you program an AI with an explicit or implicity utility function which it tries to maximize...

FTFY.

But if you program an AI without an explicit utility function, just programming it to perform a certain limited number of tasks, it will just do those tasks.

Yes, and then someone else will, eventually, accidentally create an AI which behaves like a utility maximizer, and your AI will be turned into paperclips just like everything else.