Uh... No. 

Cows don't kill the plants they eat, if they are left to graze. They trim down the leaves, but don't uproot the roots. In turn, their manure drops and provides food for various other creatures that increase the availability of nutrients for the grasses, which, in turn, grow healthier, which makes the cows healthier. It's an upward cycle of fertility and growth. 


So, if that's what you think, I'm not sure what the rest of your assumptions are.