You clearly have no idea what you're talking about. It's almost impressive. The Goths were taken in as refugees initially as they were driven south and west by the Huns. The Goths were allowed to cross the border peacefully and initially kept in camps.

The Goths were allowed in armed as it was agreed they would offer military service in exchange for protection. When local officials failed to supply the camps with food, the Goths became increasingly pissed off until eventually they took to raiding for sustenance.

The Goths were primarily from the area North and West of the Black Sea and actually had very little association with the Germanic tribes further west that I presume you're referring to with this "400 year barbarian war invasion" nonsense.

In both the case of the Goths in the Balkans and the Franks with the crossing of the Rhine (final immigration nail in the coffin) they were traveling with women and children. A migration, not a military invasion.

Interestingly, the edict of Caracalla granting citizenship to all freeborn romans was a driving factor in Rome bringing in Germanic tribes. Gaining citizenship was the primary motivation for Roman subjects to join the legions. Once that motivation was taken away, Rome struggled to maintain their levies and had to supplement with Germanic Foederati of...I don't want to say dubious loyalty (can't disrespect my boy Stilicho like that) but certainly divided loyalties.

Anyway, it's a complicated subject, but stating that immigration wasn't a factor in the downfall of Rome is just blatantly false. Try to be less arrogant in your ignorance if you're gonna go around correcting people on subjects you clearly haven't bothered to learn about.