Another good example of where it makes sense to split textures up is alpha blending. If you have some small component of the asset that needs alpha, you should split that off into another texture set/material if you can. Generally (8-bit alpha, DDS compression), storing alpha doubles the size of the texture, so if only 10%…
Its generally a good idea to split materials and texture sets based on shading. For example, you don't want the cloth to have sss while you want the skin parts to have. So the most logical way to split in this case, is to have a texture set for the skin parts, and another for everything else.