Part of what I took from this is that a smaller amplifier delivers a lot more distortion when pushed into clipping as well. So there's two problems in the picture, 1) sine wave like input and 2) more work/less cooling due to the higher distortion and noise floor.
Both of those would seem to allow more power to the coil without much of a break. Doesn't that mean it's easier to burn up a coil when pushing an amp too far? A speaker coil was designed to play with music, which is dynamic and not constant.