From everything I've researched the opposite is true. Properly managing grasslands (which used to happen naturally with large herds) makes for health grasses which develop root systems, create soil and sequester carbon.
Poorly managed grasslands that are under grazed leads to soil degradation. The answer seems to be intensive grazing followed by rest periods to allow grasses to use nutrients and grow.
I made a reply to your post on that subject of potentially transformational management of grasslands.
On this ungainly subject of grassland vs mixed forest here, I'll just remind - two hundred years ago about 60% of the earth surface was covered in mature and native forest. The figure is less than 30% today. Most of the worlds fertile crops are grown on deforested land, on the soil which native forests developed due to ecological diversity and lack of erosion. Most of the grasslands which are used for grazing, don't have soil to support demanding crops.
Poorly managed grasslands that are under grazed leads to soil degradation. The answer seems to be intensive grazing followed by rest periods to allow grasses to use nutrients and grow.
More links in my post here https://news.ycombinator.com/item?id=18287434