Can I heat a radiator directly?
Heat transfer from water to the metal of the radiator is much more efficient than the heat transfer from the radiator metal to the air. Or in the case you posed from hot air to the radiator metal.

It is also relatively simple and compact to pipe the hot water or steam from room to room and floor to floor to service a series of radiators. A duct work to move hot air in the same way would be a lot larger in cross sectional area to transfer the same amount of heat energy from the heater to the radiators.