> AIs absolutely do have goals, determined by their reward functions.

You're confusing "AIs" (existing ML models) with "AGIs" (theoretical things that can do anything and are apparently going to take over the world). Not only is there not proof AGIs can exist, there isn't proof they can be made with fixed reward functions. That would seem to make them less than "general".

Compare https://www.gwern.net/Tool-AI