Heat pumps are more efficient than they used to be (at some point the outside air is too cold for them to work efficiently), so the cold climate where I'm from is just now starting to see them included in new homes.
It doesn't feel right to talk about the "efficiency" of a heat pump system; talk of "1W in gets you 3W out" isn't right, because you didn't magic those 3W out of thin air. It's more like "4W in gets you 4W out". It seems wrong to say that a heat pump system is "400% efficient".
I thought efficiency was a measure of how much of the work[0] going into a machine is transformed into the intended output work. I suppose you could say that this heat delivery machine is inefficient if a lot of the input work is expended on producing torque, or raising heavy stuff. But even that eventually turns into heat; just in the wrong place.
[0] I hope I'm using "work" and "machine" in the technical sense, so that "work" means displacement against a force, and a "machine" is any device for converting work from one form to another. Effiency is well-defined for that kind of machine: it's just the ratio of work in to work out, the output being what you want; so "efficiency" intrinsically depends on what your intentions are for your machine. .
Those 3W didn't come out of thin air, it came from outside air.
1W of energy going into the heat pump causes 4W of heat energy to get moved from outside your house to the inside of your house.
That's the key thing to take note of. Traditional resistive heating works by turning electrical energy into heat energy directly. Heat pumps move heat energy the same way an A/C unit does, it just moves it the other way.
Essentially, a heat pump is just an A/C unit with the evaporator and the condenser flipped.
No magic, but you are pulling those 3W out of the outside air.
You can use the industry term 'Co-efficient of performance' to avoid any possible ambiguity, but it's just the same thing with a different name.
The key is the Coefficient of performance https://en.wikipedia.org/wiki/Coefficient_of_performance
However, consider the greater performance scales with generators combined with the amount of useful heat that one gets out of a heat pump can be better than converting the natural gas to heat locally - even with losses on the grid.
The key is that a heat pump doesn't convert electricity to heat (as a resistive heater) but rather moves heat from one spot (outside) to inside with great efficiency.
There's lots of ways to heat homes in ways which use way less than 1 joule of electricity for 1 joule of heat.
A PC under your desk will keep your toes warm, and maybe with warm toes you don't really mind the rest of the house being at 10 C / 50 F. With such space heater, you can turn down the thermostat for the entire house and only heat the parts you care about most. Furthermore there are radiative space heaters which direct infrared energy to a specific part of the room using a reflective dish, instead of heating the entire room using convection. In large rooms, radiative space heater can keep you feeling warm while using much less energy than a heatpump would require to heat the whole room.