Well, try storing heat for later use. How do you do this as a temperature battery?
An efficient device like solar panels are still much much less effective without batteries. In the same vein, producing or moving heat right now doesn't mean some other room or device needs the excess or inverse right now.
Nobody runs a dryer constantly, for example. If there's barely any heat to pull when it is needed, how do you solve for that? Generating heat goes against the goal of recycling it with a central system.