The Three Kingdoms is most prominently remembered in China through the novel "The Romance of the Three Kingdoms" attributed to Luo Guanzhong who lived in the late Yuan and Early Ming Dynasty. Although the novel is riddled with historical inaccuracies it points to a the Chinese cyclical historical framework where the country was strong when united, but due to immoral rulers (who delegated power to eunuchs) the empire would eventually become weak and fall due to the Mandate of Heaven

In modern Chinese history when the Qing Dynasty fell in 1911 power quickly went to the Qing's most influential General [Yuan Shi-Kai] (https://en.wikipedia.org/wiki/Yuan_Shikai). He tried to declare himself emperor of the new Republic (and may have assassinated the newly elected president Song Jiaoren). Most people did not want a return to a Emperor and so Warlords seized power in much of the southwest. When Yuan Shi-Kai died in 1916 China was broken in many competing warlords factions.

Although many tried to reunite China until 1949, and even Chiang Kai-shek (who controlled Nanjing and the surrounding provinces) tried his best, many local warlords still controlled the western and northern provinces. Mao perpetuated the idea of a strong one state on leader rule as it served his own ends. As you can see the answer is rather complicated. Rulers wished to return to the idea a strong central state with one strong leader as it served their own self-interest, but as one can see the modern history is much more complicated than that as the tension between centralized power and localized autonomy have always plagued each ruling dynasty.

China have not always being unified but it should be noted that china have more or less being unified the vast majority of the time since the second imperial period. Which is to say since the founding of the yuan dynasty in 1271 unification has being the rule whereas disunity such as the era of the warlords are big exception.

Prior to this however China experienced significant periods of disunity: notably during the period between fall of the Han dynasty and the Sui-Tang period several centuries later. It should be noted however that the idea of a unified Chinese state encompassing "all under heaven", supporting and supported by a cultured, bureaucratic scholar-gentry class is really the legacy of the Han dynasy and the idea never died even during periods of disunity.

The big addition to this idea where modern china is concerned is really the rise of Han ethnic nationalism in the 20th century on the European model which makes the concept of unity and non acceptance of disunity stronger than ever. In the same way that early 20th century Germany would not tolerate a Bavarian secession China in principle would not accept the secession of say: Sichuan or even Taiwan.

The other reason for the fear of disunity isn't really the three kingdoms period: it's the cultural memory of the era of warlords, the Japanese invasion, and the cultural revolution. There is a very strong aversion to " chaos" in China because those events have being very traumatic to the China as a nation. The lesson drawn is that a strong, centralized state which can guarantee stability is really the only way to avoid the rape of Nanking or red guards beating people up in the streets.