But yes, Germanic "immigration" both internal and external (meaning military invasions) were a major league element to Rome's downfall.
It gets more complicated, but for example at the end when the city itself fell, Gibbons claims the gates were opened in the night by some inhabitants whose sympathies lay more with the forces outside than with the Roman authority inside the city.
In many ways Rome had tried to absorb the germans, or had been forced to do so. Rome was surviving in the end with a German mercenary army and with the help of German allies. Rome became weaker and the German "guests" stronger.
Modern authors don't like to mention that Gibbons also attributed the fall to the Romans becoming an unwarlike people who relied on others to do their fighting. Or that religion softened the fall because the Germans by that time had become Christians.
I heard it was the lead poisoning from the plumbing they installed.
The Romans were master engineers when it came to moving water. Aqueducts, constant flow sewerage, etc.
They even invented lead pipe. Lead, which is poisonous, leached out into the drinking water.
Some say this contributed to a collective insanity among the ruling class, who enjoyed the very best in running water technology.
Maybe you should take another look at the book cover.
I've always found Gibbons to be a disorganized mess. Yeah there's a lot of information in there but it's not organized and its thick language and prose makes it a dreadful chore to slog through. I'll take the classic Roman historians - Tacitus, Seutonius, Polybius, Livy, etc. (if I accidently slipped a Greek historian in there sorry I'm working from memory and the point still holds.) The classical historians are easy to read, simple direct language and they don't waste time on academic speculation. They stick with interesting stuff like wars, geography, great kings and leaders, palace intrigue, assainations, broken treaties, etc. Manly stuff. I'll take that over Gibbons and his ilk any day.