Aside from sound quality there are many requirements if you want to pass all regulations and certifications. This constrains power cable design in many cases, machine-made power cable manufacturers are often unwilling to manufacture cable that won't pass regs worldwide. In the US a cable must be UL certified to be used in commercial applications, and this includes durability testing in that the cable must be able to withstand physical abuse that will hopefully never be seen in a home environment in the context of use in a high end stereo system. For example I think very few high-$ PCs are likely to get run over by a car let alone stepped on routinely! UL also prevents multi stranded and solid-core cables from approval.
Some of this is common sense, but of course common sense isn't common. For example the use of large diameter solid-core wire, this is a horrible idea! The wire will crack over time and this will lead to increased resistance, which will cause heat to build up and eventually the insulation will fail. Cables must be designed to bend! We also see some manufacturers using insulation that doesn't protect the wire from corrosion, an "air" dielectric or silk/cotton over bare copper or silver is completely unethical to offer for sale, imo. The cable will degrade over time, sounding worse and worse and eventually it may lead to increased resistance, heat and the failure of the insulation.
That said, the potential improvements that can be made by deviating from regulation include improved electrical characteristics such as lower inductance and isolation of the ground from the hot and neutral legs, as well as a ground that has less impedance at high frequencies. As mentioned, people buying an expensive cable for home use in a high-end audio system are generally not going to string the cable across their garage where a car might run it over, let alone place it in the middle of a walkway where it'll get repeatedly stepped on, the cable is handled gently and appropriately for what it is and I think this is ok. Luckily we don't see a lot of issues stemming from audio equipment, as both many cables and many components are not UL approved.
Copper quality matters a lot imo, cheap copper can sound grainy and excessively warm. The insulation matters a lot too! Again there are regulations based on the definition of IACS Tough Pitch Copper (TPC) having 100% conductivity, but for the most part high-end cables will use OFC or even higher end copper that has greater than 100% conductivity. UPOCC copper has no grain boundaries and very high purity, which results in a couple % greater conductivity vs TPC. So in most cables the quality and conductivity of the copper is better than required.
Unfortunately, there are exceptions to the copper quality issue, counterfeit cables sometimes have much thinner diameter wire than required and the metal may be an unrefined alloy of copper from electronics recycling or whatever, these cables can be very dangerous! There's TONS of fake cable (especially Furutech and Oyaide) on the market and if you get a fake PC and use it on a power hungry amp it may fail and cause a fire. I've bought a fake just to check it out years ago and even saw a audio review blog unknowingly reviewing a fake Furutech cable.