As you've noted, music will typically have a relatively high ratio between peak and average: the kick and snare drums might hit 0dBFS, and maybe the vocals occasionally, but the rest of the music must be somewhat quieter.
NB: we are not considering whether the signal is positive or negative, just the absolute value. Heat doesn't mind whether the voltage is positive or negative, which is why we use RMS calculations: Root (of the) Mean (of the) Square (of the instantaneous voltage) will return a positive value.
A square wave is always at either +[peak] or -[peak], and switches instantaneously between the two. ie, it spends 100% of its time at +/-[maximum voltage]. Since we're looking at RMS, we'll always get a positive value, and square waves end up equivalent to DC.
There are lots of sources online which will argue differently, but unfortunately they've failed to notice that their "square wave" signals contain a 0.5*[peak] DC signal, so they're (incorrectly) arguing a 50% duty cycle. Audio signals average with zero DC, so the square wave is a 100% duty-cycle signal in our considerations.
