Organic fertilizer is generally cow poop. Cows are fed almost exclusively grain corn (and then are admittedly grass finished, but generally the manure you could get is from the grain feed period.) That grain corn is... made with inorganic fertilizer.

To keep making more food, someone has to introduce nitrogen into the system. You can use bat guano (which we actually used to use before inorganic fertilizer) or you can use nitrogen fixing crops (great but typically fix much less nitrogen into the soil then people think!) or something that comes from inorganic fertilizer, whether it's been green washed through a cow's GI tract.

It's also a logistical nightmare as it's much less dense, but that's a separate problem. A huge fraction of the problems of soil health in rural places are logistical.