Better ears or better imagination? No test has concluded burn in really exists, by the way, ever tried to sell $5 wine in a $80 bottle? Imagination is a strong thing.
Just do a quick search and you'll find a number of scientific tests done on speakers (which are just big dynamic drivers) that show objective and measurable changes with burn-in time. Of course the fact that these changes are not perceptible to everyone is the reason for the lack of consensus.
Anything that moves mechanically will have a run-in period, be it car engines or dynamic drivers. The Honda NSX (old one) was famous for being run-in at the factory already so that owners could drive it hard on day 1. As for headphones, try wiggling a piece of fresh stiff cardboard and after some time it will soften up.
For headphones/IEMs that use DDs, there will be a break-in period as it is, in a simple way, just a piece of cardboard/plastic/metal wiggling around producing the sound. BAs don't have break in because the component pieces are so small that the tests done at the factory to make sure they work is probably enough to break them in already.
FWIW, I'm one of those who CAN identify 2 wines in a triangle blind test (3 glasses, 2 are the same wine). But that doesn't mean I always prefer the $80 bottle over the $5. I agree all sorts of factors affect our senses, but in a well controlled setting, many people including myself can pick out wines blind. The issue is when you start adding in scores then that becomes a problem, because none of this can be totally objective. Same for headphones.
Anyway. as they always say, YMMV and figuring these things out is one of the FUN parts of this hobby
I believe someone here did the math to show what effect the impedance of the silver cable had on the sound.
It came out to something like 0.0025dB change which will not register to the human brain at all.
I'm also not a believer in changes in sound due to cables, as long as the cables are "good enough" (meaning the impedance isn't so high that it starts hindering the electrical transmission) but the math the guy did was wrong. The cable impedance should be added to the output impedance, not the driver impedance. And there are measurable and audible differences when output impedance changes for the same headphone.
That said, I also find the difference between the silver cable and the stock one too small to matter in normal use, and it's not big enough to rule out my own brain bias as I don't have 2 ZSTs to do a quicker A-B blind testing.
Ultimately, as others have said, the silver cable feels more durable and looks nice, so I think that's already worth it for the relatively low cost (compared to other spare/upgrade cables).
Also the stock and silver jack works fine for me, and works on all my phones/tablets (ipad, xiaomi, nexus, nokia WP), so not sure what the issue is for
@Keller1 maybe you got a bad one? And not working means no sound even?