Do droppings of grazers create overly nutrient-rich soil in natural areas?

Locally, yes: just think of the latrines of horses and favourite resting places of cattle, where relatively large amounts of manure are accumulated. However, because natural grazing does not involve supplemental feeding or fertilization, there is only movement of nutrients within the habitat. If manure accumulates in one place, it leads to impoverishment in other places. This creates varied mosaics of nutrient-poor and nutrient-rich places within a single natural area.