There are some fundamental differences between clipping an amp and running a distortion pedal into it.
For one thing, the pedal probably does NOT produce a real square wave.....
The reason is that there is normally some sort of tone modification in the pedal, That generally filters high harmonics, rounding off the wave. There may also be some further tone modification, and low cutting, which turns the waveshape into a tilted, rounded-off version of a square wave. The actual average power represented by the final result is often far less than the peak.
Clipping produces a fine, clean, square, wave, how fine and clean depending on how clipped the amp is. Feedback is driving the edges to be squared up and "clean"..... And the average power represented is equal to the peak in the case of heavy clipping.
Then after the pedal comes the amp. More low cut and general EG manipulation, further scrambling the waveshape, adjusting the harmonic structure, and usually increasing the peak to average ratio.
Again, clipping is a nice clean square wave, dependent only on how much overdrive exists.
So, it is perfectly possible for a heavy pedal distortion to be VERY different from a square wave by the time it gets to the speaker.
And, it usually represents a lot less average power output than a square wave of the same amplitude. Average power is what fries speakers.
Not surprising, I'd hope, because one assumes some basic desire to be musical. A square wave is generally not the sound wanted......