They’ll almost certainly try to (and some people who are currently involved may see some success). But they won’t have their de facto monopoly anymore. And these organizations are rife with internal corruption (shocking, I know); they aren’t being run efficiently.
Without their monopoly profits, they aren’t going to be able to afford the hit squads, the bribed law enforcement, or the silence of the people who know where the bodies are buried (often literally).
Crime won’t magically fall to zero overnight, but these organizations will not be having a good time.