I do remember at one time the caution not to burn in with squarewaves as they were too different from music. So what is wrong with music for burn in? Oh you think you can use some special "hard core" signal and reduce the time for break in. Pretty damn funny that one. Is burn is better, quicker, of more quality (quality of what???) than regular music? Is it steeper edged, maybe you need slow tones to not upset the fragile nature of the system burn in is helping with. Anyone ever give any rational thought to what the heck is happening with burn in? Maybe sawtooth waves. Better than squarewaves or noise. A fundamental with all harmonics in a fourier series. A little bit more like musical signals only more so. Pink noise, why not pink noise, it also is a distribution of frequencies like music in a sense?
Why not just harden the eff up and play music till it sounds good? That way burn in, break in, listener acclimatization or baloney, you aren't wasting the life of your components on something dubious. Just play some music. Is it really that complicated? Just play some music.
Why would square waves be more harmful? Synths play square albeit less often that triangle or sawtooth waves for example. If that were true, everyone playing a synth would need to replace their headphones, amp and PA quite frequently...