It's free in the respect that you get more energy out than you put in to run it, with the caveat that you have to buy the equipment to do that in the first place.
Getting 3 units of energy out for every 1 you put in sounds like a good deal.
Until you see the price of the equipment, which may be significantly more than what the energy gain would cost over the lifetime of the equipment.
It's arguable whether it is cheaper than gas. I think electricity is 3.5x more expensive (but remember gas boilers are only around 90% efficient). The best heat pumps I think can achieve an energy multiplier of 4. But here's the rub, they only achieve that when the weather outside is relatively warm. When it is cold it is much less. And not surprisingly, it is when the weather is cold outside you use the most energy to heat your house !
There are some improvements made to the pumps that improve the energy gain (double stage), but my guess is that even with these the pumps would struggle to beat gas when the weather is cold and they push up the equipment price a lot.
As for the Scandanavian "mystery", the reason why they are used so much over there is because a) the houses are better insulated in general and so need much less energy to heat full stop, and b) they have no alternative to mains gas other than wood - the UK is quite unusual as most countries simply don't have a mains gas network which provides cheap convenient energy.
IMO the only way heat pumps will compete economically with gas is either if the gas price increases, or the electricity price falls, or the government starts taxing users of gas a lot more in some way. My guess is the government is far more likely to put a tax on gas and boilers to reduce the competitiveness of gas, than it is to lower the price of electricity.
The TLDR of all this is that its pretty complicated to figure out whether a heat pump is a good/cheap option for any individuals circumstances, and there are a lot more factors than those above in doing that calculation. I don't think it is surprising many people choose to play safe and go for a 3K boiler replacement rather than risk a heat pump, with all the complexity and potential costs associated with that option.