No, a square wave isn't 3X the power of a sine wave. The average power of a sine wave is half the peak power. The average power of a square wave is its peak power. The RMS value of a sine wave is 0.707 x peak. 0.707 is -3dB, which is half power.
It doesnt depend at all.
Leaving out drivers deteriorating from being in the elements.. Overexcursion by too low of a crossover for given applied power, and too much power in general (not to be mistaken for RMS power) is purely what destroys speakers. overexcursion will destroy the driver by bottoming out the coil and/or tearing the surround/spider. too much power will melt or deform the coil.
before anyone replies to this and says "BuT wHaT aBoUt cLiPpInG bRo"... a square wave is equal to 3x the applied power (heat) over a given cycle than a sine wave is. If a speaker can thermally handle 100 watts, and you use a 25 watt rms amplifier and send that driver a signal that is clipped to the moon and back, its still not going to blow, since that will heat the coil as if it were being powered with an unclipped 75 watt signal