I have used heat pumps in a few jobs, and they do keep the room cool, be it in Algeria or Hong Kong, I would not want to live without them.
Even in the UK I have a portable heat pump for the odd hot day, and also refrigeration units had them in the home for years, even a tumble drier with a heat pump, although that only about draws even with a vented tumble drier, when using the tumble drier at 1 kW setting, so the only way the heat pump drier wins, is by having such a long drying cycle.
To cool the house, really only option is a heat pump, and if it needs cooling, then likely loads of solar, so not too worried about how much electric it uses.
But to heat the house, often there is no solar, or very little, and also we have seen over the years how many times the electric grid has failed, I will never forget 1978 with gas fired hot air central heating which needed electric to run, and no other form of heating in the house.
Since then, I have always had a home where I had an alternative method to heat it, be it a gas fire, open hearth, or solar and batteries to provide enough energy to run the oil fired central heating.
The problem with the heat pump for heating the home, is we are relying on the grid giving us power, I can't remember a gas cut, must have had them when we moved to North Sea gas, but can't remember one.
Next is the work involved, with standard central heating, we should place a radiator on an internal wall, so the TRV is picking up true room temperature, to put them under a window, so the hottest air in the room is against the most conductive surface is daft heat wise, but we do it as often no furniture under the window, so the heat is not impeded by furniture, so it is a bit of a trade-off. But radiators are in the main silent.
Heat raises and cold drops, since a heat pump is being sold because of globule warming, clearly want it to heat and cool, so to put a radiator at floor level to cool is not going to work, unless fan assisted, so with a heat pump no option you need fan assisted radiators.
This is where the air-to-air comes into its own, as it is already fan assisted, no need for extra power to each radiator to run the fan and condensate pump. With air to water you need power to each radiator for the fan and condensate pump, the radiator on heat does not get that hot, so to get the energy out of the radiator without it being a silly size, it needs to be fan assisted.
I have had a Myson fan assisted radiator for years in my living room, and during the day, we don't hear it, but in the evening watching late night TV with the sound low so not to upset neighbours, then the fan kicks in we had to up the TV volume, OK new models have automatic fan speed variation, no need to walk to it and manually alter fan speed, but it is not silent, and I found the AC (heat pump on cool) cutting in would wake me, but could not sleep in the heat, this is one against the air-to-air, as their fans did tend to make more noise.
I have seen the problems when the condensate pump fails, including a ceiling falling down due to the condensate water.
But main problem is either ceiling has to come down, or floor needs to come up to pipe in the air to water heat pump, or it looks like an old school with surface pipes everywhere.
A single room unit
air-to-air makes a lot of sense, for the main room in the house, minimal installation disruption and can use the off-peak to some extent by heating or cooling when electric is cheap, so the central heating is only required as a top-up, on very cold days, but since is as well, not an instead, it is a cost one can do without.