Yes that is a split A/C, which is also a form of heat pump, that's not really what people refer to as heat pumps by default in Europe. A heat pump is normally an air-to-water system here, which drives either radiators or heated floors. Heating with an A/C is practically unknown in most of Europe and definitely not the desired choice for most people here (even though it would make sense).

The people who need heat pumps the most don’t have $6000+ to blow on heat pumps.

So now we’re back to government subsidies, which routinely prove to drive up the price of whatever is being subsidised, especially at the scale of residential homes.

And your solution still results in the living room / dining room and other shared spaces being inhospitable in winter / summer, so you’ve underestimated the cost at least significantly.