The union influence has diminished a great deal since the '90s. But the Genovese and Luccheses families in particular still have strongholds in certain areas (The Laborers and the Waterfront obviously at the forefront). But I expect those strongholds to also diminish over time. Not any time soon, but over time nonetheless. And I think when they're gone, they're gone (much like what happened with most of the Teamster locals).
So in my opinion, long story short and all that, the unions that are still under the mob's control will stay there but their grip will slowly diminish. And when they're out of the unions, I don't see an other immigrant group picking up the pieces. Because as a guy who dedicated 25 years of service to the Teamsters and organized labor, it pains me a great deal to admit that unions are slowly dying.
While I agree with you about the overall decline in mob influence in the unions, as well as the decline of the union movement in general, there are still some IBT Locals in New York that are interesting to watch; even in recent years. From 2000 to the present, I've counted at least 20 former Local 813 officials and/or members who were booted for their ties to the the LCN, corruption, etc. There's also been several booted from Local 295 at JFK since 2000. Local 282 has continued to have problems in recent years. Local 812 and 1181 are others.