The claim there is very specific ("In the neighborhoods where they're running businesses or collecting protection money, you won't see people getting mugged because the yakuza don't want people to be afraid to come there and spend money") and doesn't make much sense in the context of things like the Economist's article As crime dries up, Japan’s police hunt for things to do:

THE stake-out lasted a week, but it paid off in the end. The tireless police of Kagoshima, a sleepy city in the far south of the country, watched the unlocked car day and night. It was parked outside a supermarket, and contained a case of malt beer. Finally, a passing middle-aged man decided to help himself. Five policemen instantly pounced, nabbing one of the city’s few remaining law-breakers.

and

Even yakuza gangsters, once a potent criminal force, have been weakened by tougher laws and old age.

https://www.trendiee.com/news/crimes-dried-pretty-officer/