This is really the whole story of this thread in a nutshell.
People remain hyphenated as long as they choose to be insular. The big Italian influx to the US northeast was in the last of the 1800s & beginning of the 1900s. Now, 100+ years later, some of that diaspora has been totally integrated for a generation or more and other parts are still largely insular.
Ref this thread on the history of Irish vs Black discrimination, which tells a similar tale.
What this suggests for the future is that groups that choose (or are forced) to stay insular will have slow or no integration while groups that choose to assimilate will lose the hyphenation in a generation or two at most.
Here in Miami we see on the one hand a distinct Cuban society that mostly sticks together like @pulykamell’s Chicago Polish community, and a broader Latin American immigrant mass that’s assimilating at high speed.
Unfortunately what this suggests for the ultimate hyphenated group, the African-Americans, is that until we’re all a uniform shade of cafe mocha they’re going to struggle being just Americans. It will happen, but it’ll take a couple hundred years since collectively we’ve just barely gotten started on the blending process.