A clipped sine waveform is not a map of the speaker cone's motion. You are letting the notion of cone motion and speaker cooling confuse you. A clipped signal hurts a speaker not by some voodoo cone motion quirk or shadowy watts that dont help move the cone, but simply from the drastic rise in amplifier output (which usually causes failure via thermal issues, but certainly can cause over excursion as well).
Read this article:
Speaker Failure Analysis
Some highlights:
"The hazard with allowing an amplifier to clip is NOT that there is anything inherently evil about a clipped (or square) audio frequency wave but simply that the effective power output has increased - often dramatically!"
"More power always equates to more heat - never less! This demonstrates quite clearly that the idea of using bigger amplifiers to "prevent speakers from failing" is just silly - it does no such thing, and never did."