The tradition of having traveling central authority agents going around investigating corruption and 'righting wrongs', protecting the authority of the Emperor, defending the law and the system, etc. can be said to have roots in Confucian thinking. A large part of these agents was to keep everyone 'in their place' so that society could function harmoniously.

But it was also a practical must for a very large country whose bureaucracy was nominally based in the capital, or wherever the de facto seat of authority for the ruler was. The further a place was from the capital, the weaker their hold, authority, and influence on it was.

This necessitated governors and officials that were educated, promoted and appointed through the central bureaucratic system. During good times and under benevolent governors, the system worked well.

Problems were solved without having to constantly draw on the resources and manpower of the capital, lands far away from the capital were developed instead of being disorganized territories, and of course, taxes and levies were provided to the central government.

But governors were also prone to corruption. In their place of power with few or no checks on their power, far from the eyes of the capital, they had lots of room for abuses and exploitation.

Hence, the necessity of traveling agents to uphold the laws and systems.

Of course, they didn't only discipline upstart governors. They were also supposed to investigate things like possible rebellion fomenting, whether it was led by nobles, peasants, or the governor himself! They would also press issues like a province not giving its fair share in taxes through auditing, investigations, etc.

The idea was that these agents answered the question of 'if they (the governors) are watching us, who's watching them?'

These agents' use was manifold. They were supposed to symbolize that governors, while privileged with status and power, was also responsible for a great many things. The idea that one could show up and had powers to investigate, arrest or depose a local ruler was supposed to be a major motivator in not abusing one's office.

For the common people, it was an assurance that the system would and should work properly. Everyone had a place, even the governors that ruled over them. The symbol of the agents reinforced the idea of stability in the bureaucratic system.

They were also the Emperor's 'hands, eyes, and ears' as it were, to directly influence regions, officials, and policy as well as relay reliable, unadulterated information back to the throne. The imperial court was a dangerous place if you didn't have reliable sources of information.

Of course, in reality, these agents were not infallible. Some would take bribes. Other times, governors with too many skeletons to hide would scheme to divert or plot to forcibly prevent agents from entering their locales. And of course, as with any organization that has power, they were fully involved in politics, whether internally, among the agents themselves, or externally with other ministries, organizations, and rulers.

As for why Japan didn't have these?

Well, for one thing, ancient and medieval Japan have little precedent for it. For much of Japan's history, even after nominally being unified at the end of the Sengoku Period, the Japanese bureaucratic system has always been much more decentralized, with much greater emphasis on local lords than any central figure, whether it was the Emperor or the shogun.

And before this unification, politics, society and government were almost always based on the local region. People did not identify as part of the 'state' of Japan. For example, Takeda Shingen would have been of the Takeda clan from the Kai Province, even though he was incredibly close to the capital.

But during the Edo period, there were agents that did the same thing agents in Korea and China did.

They were called metsuke but their jobs were very different from agents in China and Korea. This is because really, daimyo could do whatever they wanted in their realms. If a daimyo was a brutal ruler that executed people for even the pettiest of crimes, this was not within the purview of the metsuke.

The metsuke focused solely on keeping the various daimyo and lessor lords in their place, mostly to prevent them from plotting rebellion together. Their job was to placate and pacify the samurai class, preventing threats against the shogunate from materializing.

The only 'corruption' they fought was if a province was short on taxes. Again, because daimyos nominally decided what the laws were within their spheres of influence. Bureaucracy in Japan, even after unification, was decentralized.

These metsuke were usually drawn from the already existing bureaucracy that was made up by the descendents of the winners at the Battle of Sekigahara, which shaped all of Japan's politics for hundreds of years. These men were from the 'best' clans who were rewarded for their loyalty at the Battle of Sekigahara.

Losers of this battle were often stripped of lands and those that remained were often barred from major political participation in the Tokugawa bakufu.

ANYWAYS.

During Imperial Japan, this continues with more modern agents of the modernized ministries.

The entire system of governance is changed and communication is much simpler. Central governments are able to project their authority, influence, and power throughout the land much more simply because of advances in technology.

Thus, the end of the need for the idea of 'traveling agents'. Before, in ancient times, these agents, whether in China, Japan, or Korea, might have gone on long arduous journeys to the far reaches of the kingdom to do their jobs. As these nations modernized, these checks on corruption were made much simpler by advances in communications, automobiles, trains, ships, etc.

The one organization that could be said to be a spiritual descendent of the 'traveling agents' in Imperial Japan would be the Shinsengumi, a notorious band of extrajudicial law agents that answered only to the Shogunate. With the backing of the Shogun, they were his hands, eyes and ears.

Ostensibly keeping the peace and being symbols of upholding the Shogun's word, which was law, many of their actions are fairly notorious for being brutal and downright bloody.

Fun fact, the Shinsengumi was still considered samurai, like the agents prior to the Meiji Period, BUT they allowed people not born into samurai families a chance to join.

You mean like the Japanese Board of Audit that's been in operations since 1880?