I don't know what the deal is about people saying heat pumps are expensive. They used to be a little pricier than AC units, but it's just a 4-way valve in addition to one.

I just looked it up, and I can buy a heat pump for 200-400 euros (depending on desired output), installation is ~400 euros. Why are you paying 20-30x for something identical? This sounds like a price difference created by government behavior, like with solar panels and related hardware which seem to be significantly overpriced in north america.