Why do central heating heat pumps use water to heat the house?
Every house I have been to (all in the UK) that uses a heat pump to heat the house use the refrigerant to heat hot water, and the hot water heats the house, as per this diagram:
Spoiler Standard central heating heat pump system :
Every house I have been to (most/all outside the UK) that uses an air conditioner to cool the house use the refrigerant to cool the air directly, as per this diagram:
Spoiler Standard air conditioner system :
The whole of the second diagram is contained in the first two boxes of the first, the indoor and outdoor units. Everything else in the second is "extra".
If we forget the "Sanitary hot water" for a moment, the hot water based system seems to have two large and insurmountable disadvantages:
Thermodynamic efficiency
I have worked a little in refrigeration, which is all about maximising efficiency. While I have never worked directly with this side of it, the basic gist as I understand it is that while the free energy is "trapped" in the phase change of the refrigerant it can be easily moved about without loss of energy. As soon as it goes through the heat exchanger that free energy is in the form of heat differential and you get efficiency losses. The answer is to have as little insulation as possible between what you want to control the temperature of and the heat exchanger, and as much insulation around them both as possible. All that water plumbing in that diagram looks like a lot of insulation between the heat exchanger and the people, which will only introduce inefficiencies.
Engineering efficiency
In both cases you pump the free energy around the house in pipes and put it through a heat exchanger to transfer that to the air, either cooling or heating it. In the case of the water based central heating you are carrying it in the form of thermal energy, so the pipes and the heat exchanger are the same temperature. In the case of air conditioning you are carrying it as the phase change of the refrigerant. This has all sorts of implications to the engineering/home building front: A) Lots of extra stuff, including having all the energy go through two heat exchangers B) the size the the heat exchanger in room heat exchanger. Because the water is not that hot you need either under floor heating (which is really expensive to add at build time, and needs a lot of work to retrofit) or big radiators (which are not cheap and take up a lot of space). With refrigerant you can gave a very small heat exchanger for a large output. C) There is also the point of the pipes, water needs big pipes that need real building work to fit and possibly insulation. Refrigerant can be run in small pipes that can be fed more like wires than water pipes and they are at room temperature.
There is the question of "Sanitary hot water". While there is some overlap in engineering between the two systems, it is not obvious that this actually introduces any advantage to this system. I cannot find anywhere saying why on demand hot water cannot be provided by a heat pump, that seems the obvious way, something like this but with refrigerant rather than electricity going in.
The pure air ones seem really cheap, for example here is a 2.5 kW one for ~£500. If these work to heat a house why does anyone spend thousands on an under floor heating system for their heat pump? It is so obvious that there must be a good answer, but I do not see it.
Part this is legacy systems. In some places, water is already the heating method. It's just a fossil fuel driven system, and not a heat pump driven system. Given that this is already installed, converting to a heat pump is far less expensive than retrofitting to blown air system. In the US, a lot of places were built with hot water heating, and central air conditioning retrofitted in. This takes up a lot of space, and typically fills an attic with ductwork. But many places were also built with forced air, and retrofitting in AC or heat pumps is very easy and straightforward. Also, US housing stock tends to be young, compared to many other places. This means that more places were built with AC originally. And the US has more housing with AC in the first place.
An area built further in the past will have more hot water heating, as it's an older tech. The supply chain and local crafts people will know that better, and so that's what is available. Both for new, and refits. The US housing construction, and renovation, market is just so huge that all of the various options are readily available. Your second diagram is actually what is known as ductless mini split. And is a type of retrofit cooling/heating unit which takes up less space to install. But isn't what would be installed in most new construction, as it's really kind of ugly in the room. But a system is available which has that basic layout, except that whole house ductwork and fans are used to move the heated or cooled air around.
I don't think the water heating is as inefficient as you think it is. It's extremely common in the US. Although may be less so in newer construction. Which I see less of, so couldn't really say. Also, the majority of new housing construction in the US happens in the South, where air conditioning is the main focus, and heating secondary. So you aren't going to install hot water heating there now.
