Heat losses from room will surely be the same (for given room and outside temps) regardless of whether the air in it has been heated 'directly' or via radiator, won't it?
Oh, what a can of worms you have opened. I have debated this a lot with my son, as to the Myson fan assisted radiator, and if moving air around is good or bad.
If I put sensors around the room, I see some massive differential in the recorded temperature, but this is not the case all the time, so at the moment on the table 20.3°C behind me TRV shows 18°C, near the door, 20.5°C, and TRV 90° to one behind me, 20.5°C. All in the same room. Run a fan and air near windows is same temperature to centre of the room, as to if this is good or bad, not sure. But with the house in question, single glazed windows, so wanted to leave the air next to windows undisturbed, behind long curtains, also the vents, closing them was like the song about the dampers, the heat went into the rooms just the same, and also we really needed a humidifier, I would put trays of water in the air intake. The air was so dry.
The ground floor had ducts underneath it, so air could blow under the house with the air bricks, and I do think a lot of heat lost through the floor.
It was 1978 our winter of discontent, so the electric was turned off I am sure you remember, and the central heating can't run without the fans, so the house got very cold. And no other form of heating. Since then, we have been careful to ensure we don't rely on electric from DNO for heating, last house had a 4.5 kW gas fire in living room, this house an open fire in living room, plus CH is battery backed.
So heat pumps are a non-starter for heating. The labour government actions have ensured that, not that the Conservative government actions in the way they treated the miners was any better.