Why do high current wires have fabric/nyon sheathes?
I haven't made a study of the matter, but a reasonable hypothesis is that the insulation needs to withstand high temperature, which limits the choice of materials, and the particular material chosen would not be sufficiently flexible if it were made in a solid tube rather than a weave.

For example, a quick web search suggests that materials used for high-temperature insulation may be "mineral textile fibre or fibreglass". If fiberglass insulation was not made of strands, it would just be glass, and thus very rigid.

Of course, solid glass and ceramic are also used in high-temperature applications, but you think of them as custom-made fittings rather than strange insulation on ordinary wire.