Actually, this is not the real problem. It's not the herding of animals that's creates the overgrazing. It's the large scale killing of predators. This creates huge herds of grazers that absolutely destroy the landscape. This is how the savannah and the great plains where created. To protect their herd and children; natives killed the lions, saber tooths, wolves, hyenas, big cats and bears. In effect creating the great grassy plains. Not saying that humans created all the large grassy plains; just saying they have become substantially bigger since humans are around.