Bentonite?
Yes, it tis! Give that man a Kewpie doll! *LOL*
Also "yes" again, the fine particles of clay (bentonite) do exactly textiles what they do for pottery making; cling to surfaces. Suppose of the stuff launders out easily there won't be much of a problem, but...
This whole thing began out of the need to combine what are usually two incompatible processes, laundering and softening of textiles.
Textiles laundered in soap are softer than those done in "detergents" because the natural oils and fats leave a residue. Also if the water is not heavily softened with highly alkaline substances such as washing soda, and others, fibers aren't as roughed up as they might be.
Once detergents made from man made surfactants came upon the scene there is a problem. The two main chemicals of that nature: ionic and anionic tend to work at cross purposes with cationic surfactants. The later while having cleansing properties, also softens and smooths textiles. Indeed it is the stuff of everything from fabric softeners to hair conditioners. It is also why "two in one" laundry detergent liquids such as "Rain Barrel" and others tend to perform neither cleaning nor softening as well as stand alone products used in different cycles.
OTHO clay does not interfere with surfactant or other actions during the laundering process, so it seems upon the surface a better choice.
Being as all this may, oils, fats, and cationic surfactants tend to provide better results when measured by humans and machines. You notice the Purex bottle above speaks more about "lasting freshness", than softness of texiles.