Blitz47
It really was the other way around; assuming Chinese troops could ever catch the nomads, they were generally slaughtered. So the nomads resorted to bouncing from one region to the next, mass murdering civilians/allies and burning down farmland, and running away when the army arrived.
Various Chinese dynasties could have simply rolled out the war machine and burned every inch of steppe to the ground, after killing every living creature they found (man, woman, child, baby, goat and horse), and they would have avoided tens of millions of civilian deaths on balance.
I doubt it, considering China not only tolerated but nurtured extremely militarily weak tribes like the Yuezhi who had fewer fighting age men than 1/20th the Han standing army
China had a lot of strengths- their weaknesses were poor natural resources, land that was impossible to defend (esp in North China) and being thronged with endless hordes of mass murderers.
From the genetic data I have seen, this appears to be untrue, unless the "barbarians" shared many markers with the "original" Chinese. Northern China remains one of the most genetically homogeneous areas in the world, and without a doubt the most homogeneous of Asia outside of a few pockets of 10-30k people in Northern India.
This is because aside from outnumbering the "barbarians" 50-100 to one, the "barbarians" had a habit of genociding foreign-led dynasties and courts- as well as waging total war against each other. e.g Dzungars vs. the rest of the Mongols, Northern or Eastern Wei vs. Xianbei, etc
Other posters have found problems with your post already so I won't repeat the same troubling issues that were raised.
You are not being consistent. You are saying you can simply salt the earth and prevent those steppe nomads ever live there. You also say Chinese wins against the nomads when Chinese catch/meet those nomads. You also said it's hard to find those nomads.
First of all, you shouldn't be so broad in many of your assertions as others have pointed out, it's not any dynasty that could deal with nomads problem. I was being extremenly careful and cited Han dynasty against Xionnu (forgot your way of spelling since there are too many English spelling of the same Chinese word). Let me remind you just the Han problems then.
1. The founding emperor of Han dynasty, Han Gao Zhu, tried the military method, the result was him surrounded by Xion-nu for 7 days an dnights and nearly ran out of food, essentially close to annihilation and outright lost. This is from Chinese own source so please don't gloss over again and deflect/divert the issue. Your assertion Chinese could've done it anytime, various dynasties, assume Chinese can catch nomads is simply too broad and untrue as I already found one example here showing you. It goes on
2. The ming dynasty also lost big to Mongolian. Remember 1449 AD? You might want to look up that date where Ming emperor was captured by the "barbarian".
I made the statement if we know pertinent trait of those ancient "barbarians". That is the problem. The nomadic steppe people are fluid, they move around and the stronger ones survive while the weaker one either submit to the will of the stronger one (e.g. Mongols had a lot of Turkish tribe allies in their army and Turks had other nomads when the Turks were dominating, so did Khitan, Jurchen, and many other nomads, it's their way of life, submit or perish). Those nomads, some preserved their genes in China, some in Iran, some in Europe. Eventually various nomadic barbarians became present day Chinese, Indian, Persian, middle eastern, Russian, etc. etc. You have to cite your sources on genetic studies and it'll have to be subject to strict scrutiny. Studies can be directed with a purpose and I know at least one top 5 medical school in USA even opened up a seminar to teach its medical student how to detect possible bias in various medical studies. There are lies, damn lies, and statistical lies.