if carnot diagram is drawn, it will show nothing cheap. try to recall thermal dynamics taught many years ago. heat pump works well when the exterior temp differ not much from interior temp. Namely for places like Cal and Tex, still the winters need heating. if it is freezing temperature, much energy will be spent on the mechanical part. Literally an electric heater but maybe less efficient than an interior heater by your knee. Not very logically coherent. Recall the professor's words.

thermal dynamics is a very chilling subject, basically demysterifying fundamnetally and establish a solid view of engineering. Its experiments were repeated by millions of engineering students, the rules derived still hold firmly on earth so far.