This may be true for the early Empire, but by the reign of Diocletian the Emperor was far more than an "extra-constitutional personage." There was by then a vast corpus of law that upheld the emperor's place as the official and undisputed ruler. Indeed, even by the Severan dynasty, it was accepted that the emperor was the source of all law: Princeps legibus solutus est was a legal principle established by Ulpian. So although the ambiguous nature of the emperor's position caused problems (even up to the Crisis of the Third Century), I don't really think it can be cited as a reason for the Empire's fall.
A lot of people seem to be making comments like this, seemingly stating that the Western Empire fell because it was just poorer and weaker than the East. And its true that there are a number of reasons why the Western Empire fell and the Eastern one lived on. However, I think its a good idea to try to avoid seeing the way history unfolded as inevitable. Yes, the East had a number of advantages, but when the Empire separated for the last time in 395, it was not obvious that the West was not going to be able to stand. The East was exposed to a lot of barbarians from over the Danube (Ostrogoths, Huns, and eventually Avars, Slavs, Bulgars, ect, ect) and much of the lands that made it rich were exposed to attacks by the Persian, whom the Romans saw as the biggest threat to their survival.
Also, to quote Peter Brown, "To contemporaries, the failure of the western emperors in the fifth century was the least predictable crisis the Roman state ever faced. For the emperors were not economic historians: they were soldiers. For them, it was axiomatic that the northern provinces of the Latin world were unsurpassed reservoirs of manpower. Throughout the fourth century, Latin soldiers had dominated the barbarian world, from Trier to Tomi. To the Latin speaking soldiers among whom the emperors were recruited, it was the East, with its swollen cities and unwarlike peasantry, that seemed the weaker part of the empire."
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