Only way a voicecoil burns up ... "prematurely" or otherwise ... is excessive electrical input power, converted to heat in the coil's resistance.
Now, since amplifiers are like voltage sources, power is ~V^2/R. So you've only got two options for explaining coil burn-up:
1. A surprisingly large RMS voltage may be delivered to the coil during amp clipping, as described (very well, in good detail) above. Well, "surprisingly large" ... to someone that hasn't gone through the calculations //content.invisioncic.com/y282845/emoticons/biggrin.gif.d71a5d36fcbab170f2364c9f2e3946cb.gif
2. The input impedance of the coil drops during clipping, allowing more current to flow and therefore more heat. I think there's a possibility of this, IF the sub reaches an excursion limit (motional impedance dropping to simply voicecoil resistance, allowing more current to flow through the coil, therefore more heat). But I sure don't see it from amplifier clipping.
Bottom line : Coils burn from excessive power, nothing to do with waveform shape. If you want to explain burned coils, you gotta explain where the extra power came from ... pure & simple