You're saying grazing is zero input but e.g. a soy bean farm is not. This whole comparison is off.
A soy bean farm is a bad idea, firstly. To maintain balance, you wouldn't just want to farm soy beans.
Next, grass doesn't just magically appear. It too needs nutrients.
Cow manure is one way to improve soil nutrients, but Permaculture shows us many more ways to keep the cycle flowing.
In the end, the best picture is actually that the cows grazing and the soy beans exist together in a larger system of many other products that work together in providing nutrients that the others need.
Cows, though, are ultimately unnecessary for a Permaculture style system, and we can grow food without them. Then they can just be there as our friends and participate in our agricultural systems as fertilizers, if circumstances happen that way.
Everything I'm talking about is based on Permaculture. From the Wikipedia page on Permaculture [1]:
Animals, domestic or wild are a critical component of any wild or designed sustainable ecosystem. Research indicates that without the animal’s participation and contribution, ecological integrity is diminished or impossible. Some of the activities that contribute to the system include: foraging to cycle nutrients, clear fallen fruit, weed maintenance, spreading seeds, and pest maintenance. The nutrients are cycled by animals, transformed from their less digestible form (such as grass or twigs) into more nutrient-dense manure.
Fertilizer requires manure. Without manure you need synthetic fertilizer, which breaks the natural feedback loop and no longer good Permaculture practice.
Sure grass doesn't magically appear on it's own, but it can when you rotate some ruminants around from paddock to paddock. I have a friend who has a business doing this. She drives around a truck full of sheep and revitalizes land that has been turned to desert due to overgrazing or mismanagement [2].
A soy bean farm is a bad idea, firstly. To maintain balance, you wouldn't just want to farm soy beans.
Next, grass doesn't just magically appear. It too needs nutrients.
Cow manure is one way to improve soil nutrients, but Permaculture shows us many more ways to keep the cycle flowing.
In the end, the best picture is actually that the cows grazing and the soy beans exist together in a larger system of many other products that work together in providing nutrients that the others need.
Cows, though, are ultimately unnecessary for a Permaculture style system, and we can grow food without them. Then they can just be there as our friends and participate in our agricultural systems as fertilizers, if circumstances happen that way.