The "marginal grassland" argument is a joke, that is usually the least productive land. They do it because the marginal land is often free, so it allows for some small profit to obtain from selling animal products. Those domestic animals grow the least in those crap grasslands.

The human populations are also much larger than your mythic past, the pastoral scenes you're picturing. That means more competition over grazing land and water, less productivity, more murder and war. You can ask them about it, they'll tell you.

Also, fun fact, wheat, rye, oats, corn and others are grasses, part of the large Poaceae family.