> but not in 180 AD, because that specific period happens to be well-documented?

As for "why pick 180 AD then?" it's clear that this was chosen in order to have Commodus as a villain. Commodus is shown mostly historically accurately: he really was with his aging father Marcus Aurelius in Germania, he really was a teenage emperor who was seen as immature, vain and capricious (if the historical record doesn't explicitly support "downright evil") and he really did love staging ever-greater gladiator games.