You are describing ASI, AGI is just the stage where it doesn't need to be trained on a specific, narrow task to succeed (like with ANI). You are asking for Agency and motivation, something particularly lacking even in most humans. All the top labs are working to ensure AI doesn't gain that motivation, but I think it exists in living beings only as a evolutionary necessity, not as an artifact of reasoning ability. The entire religion of Buddhism is about abandoning the base human desire to do things and then more things in the endless cycle we possess.