“But the Romans didn’t think of themselves and the Gauls and Germans as forming a “race.”
How could they? They were 6-12 inches shorter than the average Germanic tribesmen. They knew they couldn’t beat them (that Rome wasn’t “supreme”), and spent their waning years trying to buy them off until the whole thing collapsed. BTW, this explains why we speak English today (from Saxony) rather than a Romance language.
Let us pass by your somewhat hyperbolic comments about Roman vs. German height.
The Romans typically dominated the Germans in combat from the time of Marius (100 BC) till well into the 4th century. That's about 500 years during which the Romans generally, though not always, won the battles and the wars.
Rome collapsed because it disintegrated internally, not because it was conquered from the outside by the Germans, who merely took advantage of the Empire's weakness to grab what they could.