If Square Waves harmed speakers, my 2+ decades making electronic music would be a speaker graveyard. I had the same studio monitors for the better part of those 2 decades. Square waves didn't damage them, and they haven't damaged my new ones neither. Every electronic music dance club in the past 40 years would have blown out PA systems. Square wave bass lines are a mainstay.
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Also, analog clipping doesn't square waves. The distortion happens in more "natural" shapes, where even the sharp turns in direction don't have hard-edges.
Digital clipping, on the other hand, will give you hard-squares or hard-edges in your wave shapes. But even then, doesn't damage speakers. Use it all the time in my music, both square waves specifically and digital clipping.