Well, which is the better heat carrier, air or water? With that you already have the answer... The opinion about the air-air heat pump does not come out of nowhere.
What you write is simply nonsense!
The fact is, air only has a lower specific heat capacity than water. That’s why ventilation systems move m3/h and not L/h, hence the larger pipe cross-sections.
It is also a fact that we perceive heat as radiant heat or ambient heat/air temperature.
All hot water heating systems must centrally heat the water and then transport it to the room to be heated. Until then, there are heat gains, system, and pipe losses. Then the heating surface (radiator/floor heating) must reach temperature to emit radiant heat or achieve warming of the room air through convection. All this takes time, especially with systems with low supply temperatures, such as heat pumps. Ventilation of the building, of course with heat recovery, is still necessary today in addition.
With a ventilation heating system, the ventilation runs anyway and does what it is supposed to do: ventilate. In every supply air element, in every room, there is a small electric post-heating element which compensates for the heat loss that the ventilation heat exchanger causes (about 15%). Directly in the room, directly in the sensible room air, directly at the push of a button. Thus much faster than any hot water heating system, absolutely individually controllable for each room. If this electric heating element is powered by your own photovoltaic system, it doesn’t get any better.
Now comes the heat pump part of the system. The exhaust air already cooled by the ventilation system’s heat exchanger is now fed to an (exhaust) air (domestic hot) water heat pump that extracts the residual heat contained therein and converts it into hot water. Absolutely common technology, used for many years, integrated into the system at the most suitable point! Well planned, designed, balanced, and programmed, an unbeatable cost-effective and efficient system.