You don't know nomads.
As long as the Han people in the great wall do one thing, the nomads will die in large numbers. That is to ban the tea trade.
Nomads lack fruits and vegetables. Without tea, they can hardly live to 40. Han people usually support some nomads to attack another group, or cut off trade and force them to attack the Great Wall.
The Han people also use the Great Wall to block the metal trade. Often the nomads have to fight the Han people with weapons made of bones. The armor of the Han people is like this.
View attachment 778114
View attachment 778115
And you think it's wrong that nomads have high protein content. You can search for a Chinese food, Bean curd. It contains very high protein and is very cheap. Finally, the height of the Han nationality is much higher than that of the Mongolian nationality.
PS: The Huns who destroyed the Roman Empire. The Turks who perished Byzantium. They are all losers outside the Great Wall. He fled to Europe in order to avoid total destruction.