Okay, let's look at this problem slightly differently and see if it makes
more
sense.

When a small amp goes into heavy clipping it produces a signal that looks
pretty
much like a square wave. Forget about the harmonic train for a moment and
just
look at (or consider) the shape of the signal: a sudden rise to the top,
it
stays there for a while, then a sudden drop to the bottom, where it stays
for a
while, and then it repeats all over again.

There's another way to describe that kind of signal: pulsating DC. For a
speaker, it's a hard signal to handle. The speaker moves out and simply
sits
there, then it moves in, and sits there. While it's just sitting there,
being
held out (or in) by the voltage, the temperature in the voice coil is
rising,
since there's no way to dissipate the heat from the "DC" that's holding
the
speaker still. Do that long enough (even at lower than maximum speaker
ratings)
and the coil will eventually burn up.

Is that easier to grasp?

Unfortunately, it doesn't really clarify anything. In fact, it muddies
things up even more. First of all, there's not really such a thing as
"pulsating DC". That's an oxymoron. If it's "pulsating", it's by
definition an AC signal.

The rest of what you say would be true only if the fundamental was on the
order of fractions of a Hz. It's a nice idea, but it's simply not the way
it works. The voice coil doesn't care a whole lot about the motion
waveform - it just cares that motion is occurring. Whether it's a square
wave or a sine wave, it makes no difference. Also, due to the inductance of
the voice coil and the limitations of the amplifier, most speakers will
generally not move in a square wave fashion anyway, even when the amplifier
is severely clipped.