General AI

What is the point of having a General AI instead of highly-tuned(optimized) specialized software fit for the task?
I.e. the "human-like AI" vs domain-specific software

- it must be able to actually win the war with humans

Cyberdyne shill detected. Even getting to this point is really bad.

- it must decide the existence of humans is a threat to its survival

It wouldn't just decide "humans are bastards", it would compute the effect of humans being alive(pollution, waste of resources, etc) and compute the utility value of human civilization not existing.