We (humans) have not only survived but thrived. 200,000 annual deaths is just 7% of the 3mil that die each year. More (as a percentage) probably died from access to the best health care 100 or 200 years ago. The fall in birth rates is, IMO, a good thing as the alternative, overpopulation seems like a far scarier specter to me. And to bring it back to AI's, an AI "with a pathological drive to maximize an arbitrary metric" is a hypothetical without any basis in reality. While fictional literature -- where I assume you got that concept -- is great for inspiration, it rarely has any predictive power. One probably shouldn't look to it as a guideline.