I agree. A dehumidifier is not "exactly like" running a central AC and the heat at the same time. As you say, a dehumidifier is a heat pump and it's transfering heat from the cold side to the hot side. Since both the cold and hot side are in the same room, that part of the energy is constant. Since the heat pump does take energy to run, the electricity used does result in some heat being added to the room. But because the COP of a dehumidifier is much greater than one, you're moving 2x or 4X the energy that dehumidifier takes to run. Running the AC is essentially a heat pump too. Except there you're pumping the heat from inside outside, where it's lost. And then you're running the heat, ie gas heat, electric resistance heat, whatever, to make up for all the lost heat. That's a huge difference in efficiency and a very inefficient and costly way to dehumidify compared to running a dehumidifier.