It’s worked before.
In fact, studying the purpose of the Great Wall of China serves well to explain what success for the Southern Border Wall would look like.
At that time, the threat came from populations to the north that wasn’t set on invading and overthrowing China, but from small raiding parties looting borderland villages. Militarily, a raid is an attack which isn’t meant to occupy territory but to inflict some harm on an enemy before retreating back to a safe location. In this way, the harm that was visited upon the Ming Dynasty could come from literally anywhere along the empire’s northern border. Without warning, some independent tribe of anywhere from 15 to 200 soldiers could show up and ransack a borderland village or even a small city. They could take with them slaves and treasure, preventing development in the region and representing a constant drain on the empire.
So there are two possible solutions to this problem. You either dedicate an army, literally a whole army, to the entire border that could respond with reasonable force to any possible raid attempt, or, you build some static defense that could prevent the majority of such attacks. In the case of China, the solution was the northern border wall, a static option. Could a determined foe scale the wall? Sure, but the wall prevented the main tool necessary for these raids from getting over — the horse. By denying that tactical necessity, it no longer became profitable for the types of raids to occur. No longer did the region suffer from the raids, but also, the types of people who would do the raiding also died off. At the same, the army that was saved was allowed to be redeployed to other areas, sometimes to expand the borders of China, sometimes to protect them invasions themselves. To say the least, the Great Wall of China was necessary to providing the culture with much of the stability and security to become the cultural centerpiece of world history it is today. Eventually, the wall was overcome by a determined force from the north, but it still bought the Chinese more than 1,200 years of security after it was built.
Not too shabby.