Your grass-fed burger isn’t better for the planet, new study finds | Grass-fed beef has no climate benefit — even when taking into account that healthy pastureland can trap carbon

This is literally the origin of livestock farming. And it isn't just about infertile soil or difficult terrain - it's a simple matter of scale. If you have more land than you can farm, you graze livestock on it. Livestock also acts as a super important calorie sink over the winter when you can't farm.

Then there are places like Iceland, where large scale agriculture is literally impossible, and the only way to produce food domestically is to graze sheep on the small bits of vegetation which can grow in volcanic rock.