I don't understand this idea that you need to have a super-insulated building to be able to use a heat pump. These are two different discussions: the heat loss of the building, and how to make up that heat loss. Heat pumps are an efficient solution to the second part of the equation, as described by Vinny above you get 3 kW of heat for every kW of electricity you put in (with some variation depending on outside ambient temperature in the case of air-side HPs).The other benefit of HPs is you can reverse them in summer...
If the building is old and draughty, you just need a bigger heat pump, just as you need a bigger gas boiler. Improving the insulation of the building just reduces the size of heat source needed.
Am I missing something?
Yes you can (and if it were financially viable the solution for
@Somafunk would have worked), but...
The costs install such a system are currently much greater than a gas boiler. The greater the energy requirement the greater the installation cost, although it should be a non linear increase.
As most houses will use radiators, they will most likely need to install underfloor heating and a lot of insulation underneath it, or else you will be losing a lot of energy to heat the earth beneath the house.
A builder that I know has been asked to get quotes for installing an ASHP system for a large new build (6 bed) and has been quoted >£60k after a lot of haggling. His company has installed them before and says that this is typical at the moment for that size of house. I do not know what it would cost for for an older house that has a poor energy rating and requiring a retrofit.
At the other end of the scale a friend of mine who has installed 5 systems has only done it in very small houses (2 up and 2 down) and was able to purchase the units for £2 to £3k, and use his own time and experience to do all the work around the unit where the costs usually mount up very quickly. Instead of underfloor he put the pipes into the wall and so made one wall a radiator as he likes to experiment with these things. This was done after sealing the building, adding a heat recovery and ventilation system and adding a lot of insulation.
So in summary, I am not saying that you can't do what you have suggested, just that it is not currently financially viable to do so and may be impractical to do in many buildings.