Hi Hero,
Transistors in an inefficient but distortion-free amplifier can be cooled with heatsinks, speakers that are also being heated with unwanted harmonics cannot.
The harmonics of a square-wave have the same amount of power as the fundamental sine-wave frequency when they have the same p-p voltage.
If the inductor is low loss, a 2nd order Butterworth LC filter would reduce the power of the fundamental sine-wave to half (-3dB) the total output power, and will reduce the power of the harmonics to about 1/4 (-6dB) of the fundamental's power. Therefore more speakers, h-bridge drivers and LC filters would be needed to produce max sound pressure at a single frequency, when compared to a sine-wave signal.