Well, first of all, keep in mind that Chinese history was for the most part, written by officials and mandarins in the first place. Therefore Chinese history is absolutely full of examples of virtuous bureaucrats, the people writing it after all had the incentive of glorifying their own class. In Chinese historiography, one of the prevailing themes is the struggle of virtuous Confucian bureaucrats fighting against the evils of the Enunches and other political opponents. The virtuous official, who is presented as only wanting to serve the greater good of the state and the people, would often be outmaneuvered by their incompetent and evil opponents, and are then executed despite their great services. To what extent this is true is another question.

Some Great Mandarins would include:

Hai Rui: https://en.wikipedia.org/wiki/Hai_Rui

Wang Anshi: https://en.wikipedia.org/?title=Wang_Anshi

Liu Yan: https://en.wikipedia.org/wiki/Liu_Yan_(Tang_chancellor)

Lu Xiufu: https://en.wikipedia.org/wiki/Lu_Xiufu

Off the top of my head

What do you mean by virtuous? Throughout the late Imperial period, local (county level) government has always been perpetually underfunded, such that to perform even the most basic tasks required the collection of extra local taxes. This obviously blurs the line between public service and official enrichment.

But the fact that dynasties lasted for centuries should make it pretty obvious to you that things were generally working sufficiently well at the local level, shouldn't it? The local government was in charge of infrastructure maintenance (canals, roads, irrigation works), disaster preparedness (emergency granaries), public safety (bandit suppression), civil arbitration (litigation resolution), commerce (operation of state monopoly businesses), and of course census assessment and tax collection. Any serious, large scale failure in these state functions would lead to the collapse of dynasties, yet the dynasties proved to be remarkably long lived, even when wracked by violent instability at the center (Ming).

I think the evidence is pretty clear that by and large the system worked in the sense that local government for the most part was adequate to its tasks. The way the question is phrased seems to imply that for most of Chinese history the vast majority of officials were interested in little else besides pure rent seeking for personal gain and that's simply not the case.

Finally take stories of superlatively virtuous or corrupt officials with a grain of salt. China has often experienced (sometimes murderously violent) factional struggles between opposing groups of officials. These struggles are often grounded in sincere policy and philosophical disagreements, but result in large bodies of literature deifying and villainizing the figures involved. These accounts need to be read critically.