While this is essentially true, the fundamentals of what would later be considered feudalism (basically, the manorial economic system, royal delegation of fiefdoms, etc) were extant even during the later Roman Empire. Nobility as an additional social strata had been existent since the earliest days of Rome, Greece, or any other 'western' civilization (in fact, it could be arguable that such a system of social stratification is an Indo-European trait, considering its found in the caste systems of other major Indo-European civilizations, such as in Indian or Persia/Iran).
In fact, one could even argue that feudalism was something of a social innovation. It was a more informal version of the theme system that the Byzantines developed in response to the long and draining Persian and then Arab Wars. If a society is to be permanently at war, then it should be organized to be permanently at war, which is what was seen in Europe and Byzantium, government basically codifying the social changes that had been going on since the late Empire. In Western Europe you could argue that feudalism took off earlier than in the East because Europe had a ready made warrior-nobility, the Germanic tribes, to begin ruling a society that had already begun the process of deurbanization and an instant peasant population, the (insert region)-Roman people. If the late Western Roman Empire had developed a similar theme system, substituting its own soldier nobility rather than importing a German one, then it may have been able to staunch the bleeding of the Late Empire.
Semaphores, hot-air balloons, hang gliders, and bicycles (with wooden wheels). Those would be helpful for holding a big empire together. If they'd been developed in Roman times the butterflies might get rid of Charlemagne. But the empire might still fall and somebody similar might still arise.
I'm not talking about technology when I wrote innovations. I'm talking about political structures. Charlemagne's Empire was not an Empire as such, it was much closer to the kind of tribal confederacy that Attila the Hun ruled. The Franks had not yet embraced the idea of primogeniture, and there simply were no state institutions, that is no bueracracy of any kind outside of the Church. Charlemagne's Empire was just that, the Empire of one man, who was the whole government, the center of a web of personal and tribal loyalties, whose own strength, luck and long life needed to keep being repeated by an only son, over and over in order for that Empire to survive. He was the result of a series of lucky dice roles, as the only son of an only son in a tribal system that believed in divided patrimony, and as history has proven, the dice aren't loaded, eventually societies lose.