At least here in Finland a lot of people do. Very popular choice when replacing old oil furnaces (and as a "replacement" for direct electric heating offcourse)
Geothermal heatpump is something people mostly think about when building new.
Air heatpumps with the inside unit start from around 1000€ and 300€ to 500€ for the install. The price is mainly based on the size of the house (and in big houses you will need multiple or one with multiple inside units)
A fireplace for the couple really cold weeks to cut down the electricity bills are popular but people had those even before the air heatpumps so nothing new really.
You can already do most of that with a passive heat recovery ventilation system coupled to a ground/water exchanger. All systems are independent and the most high tech equipments you need are fans and a water pump
Only using ductwork for heat recovery ventilation without also using it for heating and cooling means more complexity, instillation costs, and maintenance issues etc. Further moving air allows you to use dramatically less material for heat exchangers.
Net result higher efficiency, fewer things that can break, fewer locations something can break, and lower risks of water damage to your home etc.
I am, and I am not an american, lol.
No one is heating their place with air/air heat pumps besides americans who haven't figured out that heating spaces via air is shit tier in term of comfort and efficiency