Most enrichment of the soil comes from decaying vegetable matter.
Actually, decayed roots to be precise, and particularly perennial grasses. By comparison, detritus is overrated. The problem here is mineral depletion, not nitrogen. The blood meal has iron in a particularly available form in addition to the nitrogen.
When I applied blood meal to a patch of small-flowered needle grass (Stipa lepida) at the rate of 50#/1000sft, vegetative productivity of those grasses increased 600%. Adjacent to that spot, about 12' away, I applied animal waste. In this case, it was a particularly appropriate animal waste, used cat litter, exactly analogous to the product of said Anatolian shepherd dogs and in a higher concentration of nitrogen than the blood meal. Vegetative productivity in that latter spot only doubled, if that. Worse, forb production in the blood meal area was ten times that in the cat litter area. Ungulates eat more forbs than grasses, so this is particularly important in that regard.
Considering the loss of progressing that one step up the pyramid and that if I was grazing it I would also get the waste products of the herbivore, feeding predators with herbivores and then using the waste as fertilizer is terrible soil stewardship. Your dog poop analogy isn't as good as BS... or do I need to go into the differences in intestinal microflora?