K is nice because between any X K and Y K such that 2*X = Y, the energy needed to go from one to the other doubles, too. You don't have this with C. 100°C -> 200°C is not 2x the energy.
Strictly speaking, that's not true. There might be phase transitions (which require additional energy) or the material's specific heat capacity might change with temperature, see https://en.wikipedia.org/wiki/Specific_heat_capacity .
It's not just nice for that reason, that's the reason the scale exists.