And all that inefficiency also means that the power is not only used, but turned into a crapload of heat at the transistors.
Few devices NEED a sinusoidal waveform. Computers, most of the stuff the UPS will power, use a switching power supply that only rectifies out the high voltage and filters it before switching it at high frequency through its own transformer. In this case, the modified square wave is actually better, since it charges the cap with equal potential at all times, rather than only charging the cap at the peaks of a sine wave.