The reason your nose is worst in bed
Three separate things in wool work against dust mites.
Lanolin is the fatty coating on the fiber, and its fatty acids are toxic to mites. It also coats the dead skin flakes that shed onto the pillow the moment they land, which leaves the mites nothing they can digest.
Wool then holds the air around your head at 40 to 50 percent relative humidity, below the roughly 50 percent that mites need to survive at all. And the microscopic keratin scales along each fiber physically stop them burrowing in. Three mechanisms, none of them a treatment that washes out, because all three are the material itself.
40-50%humidity held around your head
3mechanisms, all of them the fiber itself