There’s a win-win solution here: Don’t burn-in your headphones with loops of white noise and pink noise. Break them in by listening to music. A wide variety of music, if you’re worried about exposing the headphones to different sounds. That way, you give your brain and your ear time to adjust to the new headphones. And if the headphone drivers really are flexing and settling into an oh-so-subtly different sound, you’ll have arrived at that aural bliss after a few days of happy listening.
Burn-In seems like one of those things that audiophiles made up to convince us it was required.