The one I thought about (Ariston) had a CoP (coefficient of performance) of 3.0, i.e. 3kW of heating for 1kW of electricity. To compete with gas I needed CoP > 4.0. Another issue was that unless you have its inlet and outlet terminating outside the thermal envelope of your house, you are paying to heat the air it is extracting its 'free' heat from. And you needed a 12 Amp supply electrical supply, and have long reheat times (4.5 hours), etc.
So, I loved the theory, but CoP > 1.0 is the only upside and IMO that's not enough to win if you have a gas supply and have to pay the going rate for grid electricity.