It would be fair to point out that a lot of land suitable for grazing is unusable for producing wheat or other staple products. Grass grows almost anywhere, including places too rocky, uneven etc. for mechanisation to move over. But beasts can walk where machines won't be able to.

There is a reason why transhumance (moving cattle to high places for the summer to eat mountain grass and grow fat on it) has been practised since before civilization. Ötzi, the famous dead from the Tyrolean glacier, was probably a transhumanc-practicing pastoralist, 4000 years ago.