it depends - the Germanic invasions did not destroy the economic base or cultural significance.
The Western Roman economic base was damaged after the Severan dynasty and destroyed by the 3rd century crisis when the money was debased.
The Goths etc. kept the senate, the local administration etc. - they just put themselves on top
The Byzantine Goth wars in Italy in the 6th century was bad, yes. But by 800 this was revered under the Carolingian renaissance
“The Fall of Rome and The End of Civilization”, Ward-Perkins, makes a compelling argument against this. Through an analysis of archaeological remains, including seemingly humble things like potsherds and rooftiles, he shows that there was a profound disjunct in quantity and quality in every sort of material element of human existence, timed to, almost precisely, the Germanic invasions. This was not just vis-a-vis the height of Roman culture, but also vs pre-Roman times. There was obviously a horrifying catastrophe in Western Europe that sent everything almost back to the Neolithic.