It would be utterly terrifying, reducing the law to its letter rather than spirit. Ancient laws no longer applicable to present day context that most had forgotten of might be reinstated by modron peacekeepers. "Ask not what your kingdom can do for you, but what you can do for your kingdom" would be taken to the extreme - no room for individuality or special needs; some sages might aspire to attain "modron mind," utterly abandoning the self. Society might be mobilized toward the "great power of the working class", albeit slowly being stripped of humanity.
There would likely be a Hexaton serving as general of the modron army that fought alongside the king. Because death off Mechanus mean a hierarch modron won't be reborn but rather disintegrated & absorbed into Mechanus, it's possible the Hexaton and other hiearchs might be circumspect about exposing themselves (and possibly the modrons in their care) to danger, preferring to let local human constabulary handle most cases with light modron support (to ensure no one is charmed or bribed or otherwise improperly applies the law). The Hexaton would have a personal guard including one septon, two octons, three nonatons, five decatons, and 25 pentadrones.
The Septon would be like a traveling legal scholar and inspector, ensuring the law is well implemented on the regional level. It would likely have traced back a complicated legal basis to "prove" the king's just rule via ancient scrolls of birthright or concessions of territory. Local administrators would scurry to prepare for the coming of "the inspector."
Each Octon would oversee one nonaton, who in turn commands one decaton, who controls five pentadrones, then 16 quadrones, 81 tridrones, 256 duodrones, and 1,728 monodrones through the chain of command. Depending on your demographics, this might have been sufficient numbers to tip the balance in favor of the current ruling king. The Octons likely serve as regional governors, one overseeing a territory widely regarded as the kingdom's pride and joy – an embodiment of "efficient" rule and "perfected" law, while the other oversees a protectorate or recently conquered territory rife with unrest. They would rely on reports from human sheriffs/reeves or even rangers, assimilating as much information as possible in their towers (which may have portals to Mechanus).