The best sounding cables I have heard were a bare set of wires. Hardly practical in the real world, cables without shielding and insulation sound better than those with them.
We insulate cables so their conductors don't electrically touch each other. We shield them with tin foil or woven metal to protect them from noise.
None of these techniques of isolation and noise reduction improve sound quality. Air is the best insulator and a noise free environment what we hope for if we want to avoid shielding. Unfortunately, dangling conductors in the air is as impractical as hoping for a noise free environment. Insulation and shielding are necessary evils.
The problem with insulators is energy storage. When a signal is passed along the conductor they cover, small portions of the signal are stored then released in the insulation. This effect can be measured and enumerated using what's known as the Dielectric Constant. If we're building a capacitor we want that number high. If it's a cable, the lower the number the better.
Of the readily available insulation materials, Teflon has one of the lowest dielectric constants—far lower than standard insulation. But Teflon's expensive and hard to work with, which is why it's used sparingly.
In our ongoing discussion of break-in, I suspect it is this dielectric constant that changes with signal.