It has been standard in cheap rental accommodation in the UK for more than 20 years to have on demand hot water supplied by a gas boiler. They are a bit rubbish, in that the faster you turn the water on the cooler it is, and if you like deep hot baths you are out of luck, but it works and it is what a lot of people have.
Now the electric ones are ~£100. I have not used one, but I bet they are similar. If you have a heat pump that produces 3.5 kW one would expect it to be able to produce water at ~48 C at the same rate.
There is nothing special about radiators, aka water-air heat exchanges, that you cannot do with refrigerant-air heat exchangers. They are both metal fluid filled containers exposed to the air. I think you should have more flexibility with refrigerant, as it is undergoing a phase change so it transfers more free energy per volume, or something. You could make refrigerant-air heat exchangers look exactly like radiators if you wanted, and they would be at least as efficient.
If the problem is that the system is turning on and off too frequently that is purely a question of the control system. If you increase the hysteresis it will turn on and off less frequently. Of course the room will vary more in temperature, but if that is a problem at the same time as the machine is turning on and off too frequently you have a far too powerful system.
When I say forced air I mean having a fan attached to the heat exchanger rather than relying purely on passive convection. I do not mean where hot/cold air is piped around the house, I have never seen that here. The options are pump water or refrigerant around the house.
It was the person in the video complaining about noise. I think that is because the system he used had a fan at the heat exchanger in the room.
I'm wondering if the issue isn't installation and service costs? Mini splits, or central AC, pipe the refrigerant to a single location. That minimizes points of failure, and installation cost. Water systems are no more robust than potable water systems in the house. Which makes installation relatively inexpensive, as any plumber can do it. And it only has to contain water at lowish pressures.