The power/heat issue and 'jerking' back-and-forth are closely linked.
At either flat end of a square wave, the driver is not moving yet a lot of power is flowing through the voice coil. The back-and-forth motion of a voice coil is what cools it, so the only chance the voice coil has to cool while reproducing a square wave is while it's in transit between the two extremes.
Since more time is spent "excurded" (the horizontal parts of the wave) than in transit (the vertical parts of the wave), this leads to rapid head buildup.
