I always feel a little stupid or strange reading a lot of these science headlines and introductions. I wasn't aware that people considered there to be a symmetry between heating and cooling. I thought that the entire point of thermodynamics is that they are asymmetric. Even the article mentions that it's been known that heating is more efficient than cooling.
Exactly, I always thought heating raises the entropy of a system and cooling puts it back in the "more orderly" state. So of course it can't be symmetric. Just like breaking a wine glass, reversing that process takes a lot more effort. Of course I have no idea if the above makes any sense, it's just an "intuitive understanding" I somehow got.
Power to heat, waste is more heat (just not where desired?).
Power to cool is used to move the state of one side of the system to another, ideally open, side.
Though this does raise the question of if it's possible to cancel energy out. I think that's likely stopped by Heisenberg's uncertainty of measurements (and exactly matching them even when measured).