You are correct on some things, but I see some errors, the eastern part was attacked by the Huns multiple times as well as other middle eastern empires (sassanids, arabic tribes, persia, etc.). They endured long enough for the Hunnic Empire to end. The Western Empire succumbed to multiple barbarian invasion and internal problems, such as a weakened economy, the rise of serfdom, (yes you were correct on the legates seizing power but also) the emperors competed with their other eastern counterparts over numerous things, the rise of christianity led to social and religion conflicts with the pagan believers. The lack of economical trade grew to cities such as milan and ravenna to hire mercenaries, which evolved slowly into the Italian city-states. Barbarian tribes noticed the lack of legionaries on Rome's borders due to inefficient training and the farms giving the legions more weak soldiers. Yes there was plenty of Legates leading resistance movements, but the hordes of barbarians were too strong and too far spread. There were revolts in Britain and Gaul, invading through Spain and crossing over to Africa, they sacked Carthage, which led to large food shortages. Rome was sacked by the Ostrogothic ruler Odoacer. This is seen as the end of the western roman empire at 476 AD. The eastern slowly evolved into the byzantine empire over many generations. They even took back Italy and parts of Africa at one point, but could not hold it once the Ottomans sacked Constantinople in 1453 AD.