If the supply is feeding something where it is first rectified, then yes, I suppose a square wave could work.Maybe I'm missing something. I understand why devices wouldn't want spikes and dips in the power, but I don't understand why any device would have a problem with a nice square wave (providing the equivalent rms was attenuated ). Perhaps someone can enlighten me ?
Some phase-controlled devices, conventional dimmers for example, calculate conduction angle by comparing a DC voltage with a sine wave or cosine wave synchronised and phase related to the supply. If the supply was a square wave, you would have all or nothing.