> A baby babbles I guess for fun but also because it's part of the process of playing with the world to learn to cope with it and to become an effective person. So talking, walking, eating, etc, are all part of the same general activity of life, and they all have their own forms of "grammar."

Yeah, exactly. Almost everything a small child does is a directed attempt to generate training data, whether they're talking to you or talking to themselves or grabbing random things or trying to crawl into traffic.