We have the same situation with gas powered heating in the UK. There is a push towards heat pumps, but they are often expensive up front and don’t always save money in the long term (although if gas prices skyrocket this would obviously change).
I've been using a DIY air source heat pump (repurposed conventional air conditioner) for the last 6 years and the investment has been quite successful. Roughly the same bill as with gas, but I don't go through annual inspections etc. I paid ~EUR2500 for the whole heat pump installation. Unfortunately, conventional heat pumps (e.g. Mitsubishi, Daikin, LG etc) with the same capacity were priced about 3x that and as other have pointed out, were not economically feasible. Possible explanations for the latter are either marketing gimmicks (heat pumps are for the rich) or a lack of big enough addressable market.
I am not sure how easy it is to repurpose newer air conditioners that have a lot more electronics. Also keep in mind that in order to use a heat pumps efficiently, your heating system must be designed to work with relatively low fluid temperatures (mine runs at ~37 degrees centigrade). What worked best for me was a heated wall + fan convector for the living spaces and oversized radiators for the bedrooms.
