Well, it turned out there is a rather subtle difference between Yaks and lots of other domestic animals like Cows, Horses, goats, etc.
Yak, it turns out, don’t really graze as the other do. Usually the animals like cows cut the grass they eat. The grass then grows after that back. Yaks, however, don’t cut the grass. Their tongues are like sand paper. They actually scrape the grass. In this case the grass actually stays in its place, just scraped.
Why the difference? The problem is that in high Tibetan plateau the soil is very fragile. In this case, if the grass is removed by an animal it doesn’t really grow back. What Yaks do actually leaves the grass in its place and also the soil.
This is actually one of the reasons why brining regular farm animals to Tibet leads to soil loss. Yaks don’t cause this.