Part of the popularity of ASHPs in North America isn't just lack of mains gas; it's that a single unit provides both heating and air-conditioning (you use ducting for both, not radiators). This is why they were originally popular in the South and other areas that don't have very cold winters. They're also very popular in townhouses, not just detached properties.
However the latest generation of ASHPs is suitable for very cold climates--think Minnesota, northern New England, Canada other than southern Ontario/BC. The key is the correct type of pump with an inverter and a correct installation. This has been a huge boon for many as previously, if you didn't have gas, you ether needed an oil burner or a propane tank. There was a boom in ASHP installation when the price of fuel oil and propane skyrocketed.
The reason the UK government is subsidising them is that the upfront cost is substantially more than a gas boiler; people can't afford to lay out that money, even if they might save more in the long term. Funnily enough there was an article in the New York Times last week about Germany pushing heat pumps.
The heat from an ASHP is gentler than from a furnace or boiler, for lack of a better term. With a gas boiler, you can blast the heating, get the house up to temp, and then coast along till it cools off. With an ASHP, this doesn't work very well. It takes longer to get the house warm, and trying to make it warm the whole house so much so quickly makes the pump turn on the aux heat. This is electric resistance heating, and it's expensive to run, especially at peak electricity rates. So running it 3hrs 2x a day may, paradoxically, be more expensive. (If the issue is heat loss that is another problem.)