Cows and chickens cannot fix nitrogen from the air. They eat the nitrogen-fixing plants. So in a sense they don't "generate" fertiliser, they only concentrate it.
In Western Europe at least, cows are kept in pastures, which are permanently dedicated to that use and not used as fields to grow crops. All in all, cows are probably only low carbon in premodern rural contexts in West Africa and Asia for instance.
Of course you can't have cows wandering through your corn or soybeans, they'll eat and/or crush it. But if you had fields that you could rotate between pasture and planted that could work.
