This is a great question! I come from a union family, belonged to the Newspaper Guild, and have reviewed many books on the labor movement. And even I can't think of a monument.
I may toss out the question at a Labor Day barbecue I'm going to later. Unfortunately, here in the South, unions have even less of a toehold than elsewhere.
A decade or so ago, the Mobile (Ala.) Police Department was paying its force an appallingly low wage of something like $13 an hour, which shocked me compared to what they get in other places I've lived, like NYC.
"How can they earn so little for such dangerous work?" I asked a longtime resident. Her answer boiled down to three words: "No police union."