If your assumption is that the Great Wall (or the series of walls that eventually became the Great Wall) was wholly ineffective, I'm afraid you're a bit mistaken. In times where the region was unified and prosperous, the fortifications were manned quite well.

Often, it gets thrown around that the Mongols somehow invaded the Jin from the north, so the walls had to be ineffective, right? Unfortunately, the Mongols invaded from the west, first going through Tibet, then the Western Xia, and then the Jin dynasty (the Southern Song would be conquered later).

The other time that you might think the walls were ineffective was at the end of the Ming dynasty. The Ming were responsible for building up the walls into mostly the present iteration of the Great Wall, using stone and such. So then how did the Manchus invade? The Manchu invasion occurred at the end of the Ming dynasty, at the same time a major peasant rebellion to overthrow the government was occurring. "Why is this important?" you ask. Well, there was a General, stationed along the Great Wall, by the name of Wu Sangui who led the garrison at the easternmost edge of the wall (ShanHai Guan, 山海关, the mountain and sea pass, where the wall meets the sea) and was about to surrender to the rebels, who had even taken the capital of Beijing. Wu Sangui though, heard rumors that his concubine/wife might be taken by the leader of the rebels as his own, and so he made a deal with the Manchus to the north of the wall. Wu Sangui allowed the Manchus to pass through Shanhai Guan, in order to defeat the rebels in Beijing. The Manchus end up continuing to conquer China after doing this though, and many generals, including Wu Sangui, join forces with them to form the Qing dynasty, the last dynasty in China.

So, in short, the walls were not as ineffective as you might think. But "easy" ways to render them useless were to go around them or just get escorted through. They did have significant impact on decreasing the raids by steppe people along the northern border though, so there was quite a bit of use.