> The remote provinces were filled with recently conquered barbarians

The Roman Empire reached its maximum geographic extent under Trajan in the first century while the western Roman Empire fell in the fifth century, so I’m curious which of these “recently conquered barbarians” you’re referring to.

> the writing that disappeared was the writing that the Roman colonists and state brought with them where they went, including back home.

Who went back home? Any “Roman colonists” at the frontiers of the western empire by the fall of Rome would have been there for centuries; in other words, they were already “at home”. More on this in a bit.

> but throught the middle ages, Christianity kept spreading and by that period of history, where it spread, writing spread too

Christianity was also the Roman state religion at the end of the western empire, and indeed remained the state religion of the eastern empire until it fell to the Ottomans in the 15th century.

Let me give an example tying these points together. The population of Roman Britain had been Roman citizens since 212. Roman troops weren’t withdrawn from Britain until the late 300’s and early 400’s, but by that point the Britons had become a predominantly Christian population that had held Roman citizenship for over a century. So at least in Britain, it was less a story of recently conquered barbarians being left behind by retreating Romans, and more a story of a piece of the Roman Empire being cut off from the rest due to a decline in state capacity.

So what about the writing? We don’t have a lot of surviving examples of it from Britain for another couple of hundred years, which makes it hard to figure out exactly what happened during this period. What we do know is that Angles, Jutes, and Saxons arrived and effectively conquered what is now England. The “Anglo-Saxons” were still Germanic heathens at this point, and while had a runic alphabet of their own, we don’t have any surviving Anglo-Saxon literature from this period. Brittonic people survived, particularly in Wales, and we do have some writings from some of them, such as Gildas. Wikipedia notes the following:

> Gildas's work is important for reasons beyond the historical information he provides. At the time when Gildas was writing Britain was Christian. Gildas uses Latin to address the rulers he excoriates and regards Britons, at least to some degree, as Roman citizens, despite the collapse of central imperial authority. By 597, when St Augustine arrived in Kent, England, or at least most of it, was populated by adherents of Anglo-Saxon paganism, and the new rulers did not think of themselves as Roman citizens.

(https://en.wikipedia.org/wiki/De_Excidio_et_Conquestu_Britan...)

Gildas wrote at some point between 490 and 550, and even at this late point you have some Britons who still considered themselves (and one another) to be Romans. In other words, to the degree England becomes “barbarian” (in the sense of “not Roman”), heathen, and illiterate, it’s because it was invaded and conquered by illiterate barbarian heathens, not because the population reverted to their pre-Roman culture.

After that point, I do agree that the spread of Christianity likely reintroduced writing; it’s only after missionaries like Augustine arrive and start to convert the Anglo-Saxons to Christianity that we have any surviving literature written by Anglo-Saxons themselves, whether in Latin or Old English.