The Great Qin Empire only has the strength to defeat the Xiongnu, not the power to destroy the Xiongnu, after all, the difference and difficulty of defeat and elimination is not a level, especially for nomadic people like the Xiongnu, and the reason why Qin Shi Huang chose to build the Great Wall to defend the Xiongnu is because he needs to do too much to spend too much energy and resources on this, and the second is to see the difficulty and durability of the Xiongnu.
Compared with the Qin Dynasty, the comprehensive national strength of the Xiongnu is not a heavyweight opponent at all, the Qin army can be consumed for a long time, even if more than 100,000 people are killed or injured, it is not a big deal, and it will soon be able to recover its vitality, but the Xiongnu obviously do not have this strength, if they are consumed in this way, it is easy to drag themselves down, and because of this, the Qin army quickly repelled the Xiongnu and captured the Hetao Plain. However, at that time, the Xiongnu were actually retreating strategically, and their main military force did not suffer any damage, so they could launch a surprise attack on them at any time when the Qin army's defenses were lax. In this context, the Qin army inevitably needed to build the Great Wall to resist the harassment of the Xiongnu. Of course, the construction of the Great Wall is more important for the Qin State to defend itself.
During the Qin Shi Huang period, the new nomadic peoples had just risen, and there were dozens of tribes on the grassland at once, each of which said that they wanted to unify the grassland, but in fact, who had a few pounds and a few pounds did not know! At this time, if a large army expels and kills the nomads, it will only be counterproductive, not only will not eliminate many, but will promote the early unification of the Xiongnu. The Xiongnu during the period of Emperor Wu of the Han Dynasty had already been unified by Mao Dundan. After the scattered Xiongnu became a whole, although their strength increased greatly, their weaknesses were also exposed. The central royal court became its weakness, as long as the Han army attacked it and had to save, it would make the main xiongnu force have to fight, and then the effect of total annihilation could be achieved. This was something that qin shi huang did not have during the period of Qin Shi Huang.
When the Qin Dynasty unified the Six Kingdoms, the arms used were still vehicles, horses, and infantry. At the beginning of the unification of the Six Kingdoms, it was neither necessary nor in line with the situation at that time to immediately organize cavalry to go deep into the desert to destroy the Xiongnu. There was no preparation for taking the initiative to attack and annihilate the Xiongnu, relying on the Great Wall, garrisons, northwestern county emigrants and spare straight roads, which could completely control the situation in northern Xinjiang. In this way, the Great Wall was built first, followed by the immigration to occupy the county, and then the garrison was defended, and the thousand-mile straight road was prepared, which was already the perfect defense of the northern Anqin border. In this situation, the Xiongnu would not be annihilated for a hundred years later, when the Xiongnu worked hard to plague China.