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The reason this is "OK" is that they move heat from one place to another. They do not generate heat from some other form of energy.

Sure they do, more heat energy is rejected to the outside world than was removed from the air inside the house. It came from the "work" (which could be a gorilla turning a crank. :) ) needed to pump the heat "uphill" from cold to hot.

"needed to pump the heat "uphill" from cold to hot"

I don't know if there's a point in discussing this with you, you clearly don't understand the physics. Of course There are IR losses which end up as extra heat on the hot side, however the bulk of the heat transfered comes from the cold side, not from IR losses.

An analogy to a refrigeration system would be a conveyor belt that moved a bucket of hot water from one side of the room to the other. Although it does take power to run the conveyor, that power is not directly related to the amount of heat transfered.