I think that you make an interesting point - that these transformer models can produce reasonable text only freed from context, and generally the useful thing is to produce reasonable text taking context into account.
But how far are we really from going beyond the five minute conversation you mention? What if you combine a transformer text model with a chess engine to produce a chess tutor? It doesn't seem like we are too far from a computer program that could teach chess from first principles (i.e. learn chess itself, and teach it in a meaningful way).
Maybe in combination with economic models, it could teach economics?
What else? Perhaps in combination with wikipedia it could teach subjects such as physics or biology? But it would just be regurgitating in that case, not "understanding" what is in wikipedia. We need an existing model to tie to the text generating capability. So what if you take an alpha-go-zero approach to model generation - instead of a human creating the model, it is developed through adversarial learning? Theoretically then, anything that can be formulated in a contest or game could be "learned" and modeled, and then combined with text generation to be taught. That seems pretty powerful, and not so far out of reach.
(Also, I love the idea of letting GPT reply to work emails for a day. Someone should set up some experiments to actually do that, and find out what happens. I bet that even though it would be a disaster, we would learn a ton.)