On an extremely cursory level this is inaccurate; "China" grew geographically during the 3000 year period between the start of the Zhou dynasty and the end of the Imperial era in 1911, and many of these additions were due to people who considered themselves "Han Chinese" invading areas where the people did not consider themselves "Chinese". This fact can't be reconciled with the idea that Han Chinese people were incapable of conducting military operations "outside their borders".

During the Zhou dynasty period from 1046-258 BCE the Chu and Yue kings considered themselves co-equal to the Zhou kings and had languages and customs that late Zhou-era and early Han-era writers considered foreign (specifically the author of the The Record of the Warring States and Sima Qian in the Records of the Grand Historian, respectively--more specific citations as I find them). Xin Shi Huang conquered the region and declared it part of China, but after his death the interregnum was marred by the Chu-Han contention--essentially a civil war between leading powers in the Han North and the Chu South to seize the machinery of the Xin empire. Only thereafter did people in South China begin to be referred to as "Han" and addressed as a part of larger Chinese civilization. Clearly this was a massive military campaign by a Han ruler to conquer a bordering state, far from simply "securing their borders".

I'd also mention that Vietnam was a province of the Han dynasty and subsequent Southern dynasties during the period from 111BC to 544AD, hardly a "miserably ineffective" military campaign considering they were ravaged by tropical disease and weak supply lines during their multiple campaigns to control the region.

Similarly, the Korean peninsula saw several fantastic reversals for Han, Sui, and Tang generals alike--but after years of campaigning, most of Goguryeo's northern territories were fully integrated by the Tang after Yeon Gaesomun's death in 666 and the subsequent defeat of Goguryeo by a Tang-Silla alliance. This was also a successful military campaign that brought foreign lands under Chinese suzerainty.

To their Nothern borders this argument is slightly more accurate; the nomadic empires of the Steppe have at various times allied with, partnered, threatened, invaded, and even conquered the North China plain, and their cultural legacy throughout North China clearly shows the military and social success of steppe societies over their Chinese counterparts. Nevertheless, portraying this as a one sided exchange ignores the times in which Han polities extended their influence far into the steppe, like the maintenance of the Gansu corridor deep into Central Asia during the Han dynasty and the later periods of disunity, or the incredible military successes of Emperor Wu of Han over the Huns.

TL;DR That's not true, they just conquered a lot of it so hard we don't even realize it wasn't originally China.

There are two problems with this question.

The first problem is that it assumes that China has fixed borders, akin to a modern nation-state. If you take into account the fluidity of the border, then the number of successful military operations should also rise accordingly.

To give a few examples, the Han inherited the territories of the Qin. In 138 BC, during the reign of Emperor Wu, the Han invaded and took over Minyue (modern day Fujian). In 111 BC, the Han absorbed the kingdom of Nanyue (which encompassed modern day northern Vietnam, parts of Guangdong, Guangxi, and Yunnan). The Han-Xiongnu War fought during the reign of Emperor Wu also saw the Han expanding into the Hexi Corridor.

The Tang at its height was similarly able to project power outside of China Proper. To the north, the Tang subdued the Tujue while to the west they conquered all the way into Central Asia and even fought the Abbasids. During the reign of Emperor Gaozong, a Tang-Silla alliance destroyed Goguryeo and the Tang even annexed Goguryeo for a brief period of time.

The early Ming under Yongle conquered Vietnam and held it for several decades (ultimately choosing to withdraw due to attrition).

The second problem is how do you define effectiveness? What makes a military operation effective? If conquest and addition of territory is what you consider to be an effective military operation, then Chinese military operations post-Han would have mostly been failures. But one has to remember that many Chinese military operations were not aimed at capturing new territories. On the other hand, if achieving the campaign's intended purpose is considered effective, then China would have had many effective campaigns.

Also, keep in mind that China expanded quite a lot under the non-native dynasties of the Yuan and the Qing. The Yuan defeated the Dali Kingdom and incorporated Yunnan into their empire, while the Qing defeated the Dzungars and annexed Xinjiang.