Another interesting thing here is that the model presumably has some understanding of the passage of time. That's one thing that can be odd about chat models, in that they will respond the same no matter whether you respond a second later or a month later.
I think even for text models, "streams" could be useful. Perhaps if the LLM sees too long of a pause after explaining something and asking a question, they could interject a "do you need help?" or something. Pure chat GPTs don't have that ability.