Heating home by blowing hot air in to desired areas
They already have that.  It's the dominant system in use in North America... but I don't think you want it.  The problem is, the pipes are enormous.   - like 4&quot; x 12&quot; (100 x 300mm) per duct, with a dozen ducts.
We joke, and call that thing a &quot;duct-o-pus&quot;.
That is why businesses have drop ceilings — to hide the monstrosity of ducts above.
Fat pipes
Now, the traditional North American approach was to have a fuel furnace with an air-air heat exchanger, then a powered &quot;air handler&quot; blower to force air through the heat exchanger and ductopus.   When air conditioning was added, its evaporator (cold side) coil was added just above the furnace heat exchanger.  With &quot;traditional&quot; heat pump systems, the fuel pump coil replaces the air conditioner, and emergency electric heat strips replace the fuel furnace (or not).  But we still have the duct-o-pus.
That system is exactly what you say you want: a heat pump in a central location that uses air as the distribution medium.
Thin pipes
In North America, the new trend is to &quot;slay the duct-o-pus&quot;, stop using air as a distribution medium, and use freon itself.   Those units are called &quot;mini-splits&quot;, and simply require a 1” hole for the Freon lines.  They use a central compressor and have a heat/cool unit in each room.
Water interchange
Another method seen commercially (think: hotels) is to plumb service water around the complex.  Then have standalone heat pump units which interchange heat with the service water.   The heat pump units can be either per-room, or per apartment and have their own ductopus.  Then, a central facility at the complex has some mechanical plant to return the water to a &quot;normal&quot; temperature of around 30C, either by running through cooling towers, or heating it with fuel. As an alternative, it can have a &quot;ground-source” for temperate water all year; a running stream, seawater (this works for boats, obviously), or favorable aquifer conditions.  That is the only way water interchange makes sense for small operations.