I haven't read all of this thread so my point may have been repeated (and I'm sure it has) but I think it may be necessary to apply a little bit of legal philosophy to this.
Any governing body like a government or the WCA has to make sure their laws or rules do not give the potential for cheating to occur, even if a proposed exception to a law is better on balance. Even the slightest potential for loopholes to be found and cheating to occur is enough to make such a proposal illegitimate. For example, when it comes to standardized testing like the SAT, they require photo IDs because although the chances of people impersonating others is small in comparison to the nuisance it would be to require kids to bring IDs + potentially turn them away for not having them, the integrity of the test has the potential to be compromised and there seems to be no other way to ensure that the person who is getting a specific score sat in that testing room and took the test. So in the case of the WCA, I think we can all agree that the integrity of records or solve times are probably the most important thing (especially when we compare it to the marginal benefit of the comfort of listening to music), and even a slight potential for there to be cheating should be enough to reject it.
So now, I'll give a bunch of ways people could cheat, all of them unlikely to result in a record but all reasons nonetheless for how people could cheat, and potentially get good at:
-people talking about scrambles through the earphones (this would make the problem of talking about scrambles less able to be regulated and more real-time)
-outside help (i.e. telling someone a pair is in the back that they can't see)
-saying algs/their recognition
-you can never verify what exactly the person is playing through their headphones
In the end, we should compare it to the rule that states that competitors cannot have the screens of camera equipment facing them. It obviously can create an advantage, despite how small, that could be practiced enough that someone could exploit it, while at the same time providing a marginal benefit to the solver by allowing them to ensure their cube is in frame, much like the benefit you get by listening to music.
EDIT: just want to respond to the arguments that talk about how there are other things that could give people advantages such as tattoos or cochlear implants: a) those things are not controllable whereas with allowing audio equipment it is, b) you can't just exclude a decent amount of people from competing solely because of those things, and c) there's only a slight benefit from listening to music, whereas getting rid of those other things would require excluding competitors altogether, which in the end is worse