I understand the workings of steam and hot water radiators, however there has been a nagging question in my mind about why we first heat water (for steam or hot water) before we heat the radiator. Why can't we use hot air to heat the radiators? For example, why can't I hold a propane torch at the bottom of an inlet opening of a radiator and heat the radiator that way? It seems to me that the radiator would heat faster and more efficiently that way.
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.
Temperature and Heat Energy are two different things. Air will heat up very quickly, but holds relatively low heat energy (low mass), so it will cool down just as quickly and transfer very little heat to the radiator, which in turn will not transfer much heat at all to the room. Think of the heat generated by a candle - directly over head the air will burn. 3 inches higher the air is a bit warm.
You'ld need a continuous flame that never shut down in order to transfer enough heat via air to the radiator to warm the room. It could never shut off, because the air would cool down almost immediately.
Water, however, holds a LOT more heat energy for its temperature (high mass). It will heat up the metal of the radiator and the radiator will stay hot as it transfers the energy to the air, since the air requires less heat energy to heat up. You'll take more heat to heat the water at first, but the water will stay hot, and the flame will only need to come on occasionally, while the radiator and all that water will stay warm.
Further forced air systems are effective because the air is mixed up in the room. ALL of the cold air in the house ends up running through the heating system. Radiators rely on passive heat transfer. Putting hot air in the radiator just won't do the trick.