I like the potential of the idea. In Western Europe, the "Dark Ages" were characterized by the rise of 'barbaric nations' and mass destruction (pillaging) of civilizations. It gave rise to monastic orders prioritizing the preservation of knowledge (through manuscript copying, both religious and classical works [such as preserving the writings of Aristotle and the annuls of Julius Caesar], which later developed into the art of illumination during the Medieval period). What if science tech not only had to be discovered, but kept (maintained)? Copies of one's tech (like blueprints, recipes, and so forth) had to be stored in science districts. If a player lost "all" his/her science districts, some of the tech could be lost (the player would suffer a setback) and had to re-discover some lost tech (perhaps at an accelerated rate)? It would also explain why spies had to infiltrate science campuses - that's where copies of the tech is stored.
During the Dark Ages, it was also a time in which barbarians were much more frequent and preserved knowledge was lost (or scarce) just as we also saw the rise of heresy and divergent religious movements ("cults"). There have been great "Revolution" mods done for previous Civ games, but those focused on just political division. During the Dark Ages, Western Europe also saw the rise in these new religious teachings - not from a foreign religion, but from a 'new teaching' or 'new interpretation' within an established religion.
So how could something like this be implemented in the Civ 6 game? Illumination could be a tech discovered (with faith and culture bonuses). It could be the 'technology' for making copies of tech for multiple campuses. Create a Scribe who makes copies of tech for all science campuses. Create a Monk who makes copies of religious scrolls for all holy sites (protection against heresy). I'm not sure about what the best method for the game mechanic would be, but that's just one way it could be done.
And just as we see empires rise and split (ie. revolution and/or civil war), the same can happen in a religion (the rise of a religion and then a "new teaching" comes on the scene to split the religion and give rise to cult followers (every world religion has cults where its believers claim to follow the 'true' and/or 'improved' way). Just as we see "barbarians" arise and we see 'barbarian units' show up when there is unhappiness, so too, could 'heretics' show up who try to 're-invent' an established religion. Maybe it could also make a 'religion' available during those Dark Ages to the player who hasn't started a religion yet (being formally adopted by a civilization) and who would be, in games terms, the sworn enemy of the civilization with the 'founding' religion.
So a DLC could further develop the religious aspects of Civ 6 for a type of "civil war" within religious systems and further tweak the barbarians into a real, nation-conquering (or at least, pillaging) threat. Illumination being used to preserve tech and a religion's 'true' teachings during a time of barbarian invasion and lost knowledge.