The MIL-W-5665 cotton webbing has been replaced in technical applications by nylon webbing such as MIL-W-4088. In fact, at the same width, nylon webbing is three times stronger.
However, MIL-W-5665 is comfortable to the touch and does not melt. It continues to be used in the manufacture of suspenders, backpack straps, and many other products that come into prolonged contact with the skin.