I thought I had explained it, but I'll give it another go....
What is a clipped signal? It's a square wave with a lower crest factor that carries more average power over time. This is the key: more average power over time.
A speaker can dissipate a given amount of power that varies with several factors, including (but not limited to) frequency, excursion, and motor design.
The speaker is capable of dissipating a given amount of heat over a given time frame. How is it damaged thermally? By receiving input current that exceeds the amount of heat that can be dissipated over that period.
If the average power over time delivered by a signal is below that speaker's limit, it will not be damaged. It doesn't matter if the signal is clipped, saw-toothed, sine, etc.
Clipping is relevant in that it carries MORE average power over time than a sine wave, but if that falls below the amount the speaker can safely dissipate, the speaker will be fine.