More immersion breaking than people everywhere suddenly acting like they're from Latium? Or moving the capital back to Rome, when even the Romans had relegated it to a (granted, fairly posh) backwater by 400AD?
You might say that Latin as the language of state and correspondence in the middle ages is actually better for immersion than the slew of native languages we're using now.
As for Roma, the place is in ruins but they're some pretty monumental ruins still. You've got things like horse breeders inside the still largely intact Forum of Nerva, etc. The monumental center is basically ruralized, but still there. I could see a triumphant Empire trying to rebuild it.
After all, that "fairly posh backwater" in 400AD was still the center of the Roman Imperial system. The emperors never came around and the imperial court wasn't there, but it was still the lynchpin of a tax spine that drove the entire western Roman economy via the grain supply. To say it was unimportant is to put an undue importance on where the guy with the fancy hat was sitting. Or, in this case, the idiot child with a fancy hat (sorry Honorius, but you kind of suck).
That importance had vanished by the middle ages (papacy aside), but the symbolic importance is still there. I think that's really the idea. In SWMH, Roma has full holding slots but I almost wonder if it should have fewer holdings like in vanilla and force the player to try to rebuild it (or burn all those pesky churches).