Step 1: Clarify what hardenability actually measures.
Hardenability is not how hard the steel gets, it is how deep the martensite penetrates for a given quench, in other words, how forgiving the steel is of a slower cooling rate. Improving it means shifting the TTT curve's nose to the right, buying more time before pearlite or bainite can beat you to it.
Step 2: Compare the levers available.
Increasing the cooling rate is a process choice, it helps you hit a given hardenability target, but it does not change the steel's intrinsic property at all. Longer heating time slightly coarsens the austenite grains, giving only a marginal delay, and often hurts toughness. Adding carbon does slow diffusion somewhat, but its effect saturates and excess carbon just makes the steel brittle.
Step 3: Why alloying elements dominate.
Elements such as manganese, chromium, molybdenum, and nickel dissolve into the austenite and interfere strongly with the diffusion of carbon and iron atoms needed to build pearlite or bainite. This pushes the TTT nose far to the right, sometimes by orders of magnitude in time, so even a comparatively gentle oil or air quench can now beat the nose and produce martensite through a much greater section thickness.
Step 4: Conclusion.
Because alloying elements act directly and powerfully on the diffusion kinetics that govern hardenability, they are by far the most efficient way to increase it compared to simply changing the cooling rate, heating time, or carbon level.
\[ \boxed{\text{Adding alloying elements}} \]