[MobiusHorizons]

Yes heat pumps move heat that already existed from the cold side to the hot side, but they also consume some energy to fight entropy, meaning they pump more heat to the hot side than they remove from the cold side. This is a net heat gain, equivalent to the energy consumed in running the AC. The value may be considered negligible compared to other sources, but it can still be on the order of 500w per room, which adds up quickly if everyone is doing it.

Of course air conditioning is reasonably well suited to be a solar load during peak hours, but in most parts of the world if everyone just installed AC units like are common in many parts of the US it would mean a huge amount of extra fossil fuels burnt.