Well, I don't know about headphone cables, but I remember back in 2011-ish when my father was doing his research on what speakers and amp to buy for the living room. So among other things we end up going on a high-end audio show in Athens and we spoke with a few guys to book listening sessions for stuff he was interested in. One guy in particular that owns an audio store in Athens set up a pair of Focal speakers whose exact model I can't remebmer, but they were great and very similar to the Viennas my father ended up buying (I even liked the Focals better, from what I remember). So when he saw we were actually interested in them, he started trying to sell us some expensive cables too, with the classic sales pitch that "if you're gonna get a pair of 2000€ speakers and an amp that costs about as much, you don't want your performance to be compromised by sub par quality cables". Then out he pulls the box of fancy cables. I distinctly remember a pair of banana plug speaker cables that were alledgedly made of silver and with high karat gold contacts and were thicker than ship rope, and a power cable that was twice as thick as that. Together that set I think cost about 600€ (or was that just the power cable? I don't remember). He lost me right when I could hear absolutely no difference. Like, zip, nada. It wasn't a case of the difference being too small to justify the price. It either did absolutely nothing (which would be my bet), or if it did something it was beyond my ears' ability to hear.
Ever since then, I've been quite sure that, if a cable is going to make a difference to sound, it's probably for the worse. Maybe a high resistance cable that messes with a headphone's impedance would hinder sound quality and then any proper cable would solve that and be an "upgrade". But if the cables you use meet a minimum quality standard... Then my guess is that that's about it. That's just my 2 cents though.
PS : Bar any unexpected delays, I'll receive my pair of 58x tomorrow. I'm excited.