I think our goals come in because we have evolved drives vs. being programmed, not because of processing power.

At the same time, giving an AI a goal is the moment when we become subject to an indifferent genie who doesn't share our values.

In terms of your original question "what use would they have for us?" I guess my answer is something like: if we program them correctly, helping us will be their only goal. If we give them other goals, even slightly off the mark and don't have a tightly integrated way to course correct (like the neural lace), then we will be like ants crushed by an indifferent boot-heel.