According to the UN's Food and Agriculture Organization [1] "just less than half the world's usable surface is covered by grazing systems" and "Grazing systems supply about 9 percent of the world's production of beef and about 30 percent of the world's production of sheep and goat meat."

Doesn't seem like such a clear win for cattle. They do note that "For an estimated 100 million people in arid areas, and probably a similar number in other zones, grazing livestock is the only possible source of livelihood.", so not everyone might be able to afford a vegetarian diet, but 91% of beef seems replaceable.

[1] http://www.fao.org/docrep/X5303E/x5303e05.htm#chapter%202:%2...