[Aachen]

You're drawing the wrong conclusion from the right numbers.

Sure, a heat pump with a COP of <2 is basically broken, but consider on how many hours of how many days it's actually going to perform at such a poor efficiency level.

Overall, your greenhouse gas emissions will be an order of magnitude below gas heating. Today, or at least until recently, it's about break-even at a COP of 3 iirc, but with solar and wind being the targets, it's going to be near zero by the time a heat pump bought today goes end-of-life.