A sinusoidal wave is the only wave shape that contain a single pure frequency. Any other shape, including modulation is amplitude imply that some harmonic (waves of higher frequency) have been added. Sinusoidal signal is the smoothest signal and form a basis function. Basis function means every other continuous periodic function can be expressed in terms of sines and cosines. We would want to have most fundamental signal which cannot be decomposed further as your power signal.