Why Instantaneous RF power is proportional to the square of the signal's amplitude, so any scheme that changes the envelope amplitude changes the power level moment to moment. Amplitude modulation (including SSB, which is a form of AM) does exactly that: the modulating audio rides on the envelope, and power rises and falls with the voice peaks. That is why AM and SSB transmitters are rated in peak envelope power rather than a steady carrier power.
Watch out Frequency and phase modulation are tempting because they do carry information, but both are constant-envelope modes: only the timing of the wave changes, and the amplitude, and therefore the power, stays the same. There is no standard mode called power modulation.
Power follows amplitude squared. FM/PM keep the envelope flat; only AM makes the needle swing.