Crime on Yamatai is low for a reason: the Local municipalities and the YNP are always quickly on top of new developments. 'Disorganized' or petty crime is often dealt with efficiently (and silently) and often gives the most evidence, making these crimes easy to handle. Unfortunately, crime still exists in the organized underground, where money, influence, and tempered violence paves the way for continued industry in illegal slave and drug trades.
Combating organized crime syndicates takes time however, as these organizations are good at covering their tracks. This means that while the YNP and local municipalities may know of their existence, they cannot prosecute them effectively. Instead, they do their best to keep their impact to a minimum and an eye out for when these organizations slip up.