The khadag arrived in Mongolia with Tibetan Buddhism, where the same object is the khata, and it settled into a landscape that already had places to put offerings. The ovoo predates the arrival of the monasteries. So does the practice of marking a pass, a spring or a prominent tree with something left behind. What the khadag did was give that practice a standardised, portable, visually striking material, and it took over.
The result is that a single object now moves freely between contexts that scholars separate and that Mongolians generally do not. The same silk goes on a monastery image and on a cairn at the top of a pass; the same gesture serves a lama, a guest and a mountain. Attempts to sort Mongolian religion into a Buddhist layer and a pre-Buddhist layer run into the khadag almost immediately, and the object is a fair argument that the layering is more a scholarly convenience than a lived distinction.
Practically, cloth weathers. An ovoo in regular use accumulates offerings in stages, faded and shredded silk under fresh, and a well-visited pass carries a considerable depth of it. Nothing is cleared away, because clearing it would undo the offerings, so the cairn records its own use.