Well but you need to consider that the "Pre-German" Nations people considered themselves as Germans (maybe except bavarians which always have, some even to this day, feel a little different about it, more like bavarians first and Germans secondly if I could put it this way). And therefor the German identication of it's people is much older than the founding. But well, calling it "Pre-German" times is fine I guess. Still without the pre german times, there would be no easy unity as it happened in 1871 and therefor plays a big role in our history as well. After all, besided a countries borders and government, its the people that make it a country after all. And the movement towards a united country was not just a dictated from the top, but also a desire of the German people across the different tiny "Roman" Empires.
Between the downfall of the Romans and the founding if Italy where like 1000+ years so it's hard to compare it imo. But anyways, Italians see the Roman Empire as part of their national history, don't they?
I agree that the comparison between EU and Germany doesnt match perfectly tho, but it has it's similarities nevertheless.