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Right, a coefficient of performance (COP) of 1 is equal to 100% efficiency. A heat pump typically exceeds that, so your COP 2 heat pump is 200% efficient (useful heat divided by work required). If an electrical joule cost the same as a natural gas joule, the heat pump would definitely be more economical; but in real life it's not so straightforward.

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If you're running your electric heating from a natural gas-fuelled power station, which has an efficiency somewhere along the lines of 40% (if you're lucky), then using a heat pump with a COP of 2 means you are heating your home with 80% efficiency. Modern gas central heating systems can be >90% efficient.

Alternatively, if you go by the relative price of electricity compared to natural gas, typically electricity has three times the price for the same amount of energy. In that case, you would need a heat pump with a COP of >2.7 to make heating cheaper than using a gas burner.

Such heat pumps do exist now. The benefit is that if/when the electricity grid transitions to renewables, you are sorted.