In case you are wondering whatever happened to Big Tim, syphillis took care of him.
Not only that, but it made it difficult for all the gangs to operate "protection services" on local shopkeepers. After all, how are you going to get a shopkeeper to pay protection money, if he has a gun and can shoot your goons before they can wreck the his place of business. An armed shopkeeper violated a thugs right to a "safe workplace".
The Sullivan laws were fashioned by the thugs, for the thugs. The honest and the innocent be damned.