I have a bachelor's degree in Chinese Language and Culture and a Master of Arts in International Studies with a focus on China. I studied journalism for a semester at Peking University and lived three years in Shanghai.

The tendency to name things like this is a very, very old habit and is rooted in the literary and philosophical history of China. In fact, the most influential books in Chinese history, the memorization of which was required for social advancement, are called "Four Books and Five Classics" (四書五經), written before 300 BC. "Three Character Classics" ( 三字经), written in the 13th century, formed the foundation of early elementary education in China. The foundational texts of Chinese literary canon (eg Romance of the Three Kingdoms, Journey to the West, etc) are called "Four Great Classics" (四大名著).

As I said before, memorization of the Four Books and Five Classics were required for the Civil Service Examination (also called the Imperial examination), which were like an extremely early version of college entrance exams that started in the Sui dynasty (581-618 CE). Scoring well on the Civil Service Exam, which was only held every few years if you managed to pass the local exams, was one of the only ways you could improve your social situation-- the son of a poor farmer might do well on the exams and become a government official-- so it's no surprise that many people studied VERY HARD for these exams (the problems with modern entrance exams in China, Japan and Korea is rooted in this history, where extreme importance is placed on education, memorization and exam culture).

Naming things in this way-- Four Books and Five Classics-- helps students memorize. It sounds silly, but you know exactly how many books and classics you have to learn! Following this naming convention, especially when it's something you want the general population to remember, helps people learn. During the Mao era, Confucius was looked down upon. As China had a series of defeats to the West and to Japan, they believed these defeats were rooted in their backward culture. They were memorizing Confucian classics while Japan was developing firearms. However, you can't completely annihilate your history and culture, so these naming conventions continued. The usefulness of these numbered names shows itself in the Four Pests (除四害) campaign of 1958. If you want your population to act on these policies, they need to know what they are. Names like that tell you almost instantly what the goal is, and quantifies it. When your idea of learning is rooted in memorization, titles like these are natural. They simplify difficult concepts and make them concrete.

Something that gets missed in English translation of Chinese writing/speaking, is the syllabic element. You'll notice the titles I threw out are all 3-4 characters long: Extremely easy to remember, even for small children. Part of the beauty of the Chinese language and Chinese poetry is the amount of information that can be conveyed in very few "words" (or characters). Many classical idioms/proverbs in Chinese are only four characters long (called chengyu, 成語) and many are basically four-character summaries of entire stories, so they don't mean anything on their own unless you know the poem or story it references. Well, you really only need to hear the story once for the chengyu to make sense, and once you know the chengyu you can basically recite the story back since the chengyu encompasses the primary moral. In that way, the titles of the policies kind of become chengyus of their own, an abbreviated way of expressing a much larger message.