Imagine 5th Century Roman reaction to the fact that a country named Turkey now occupies Byzantium and that Constantinople is now Istanbul? There is also the issue of disease. Keeping 5th century Italy isolated for awhile at least not only protects their culture from the shock of the 21st century, it also protects the modern world from diseases long eradicated that modern people no longer have a natural immunity to like small pox. Imagine that same hapless German tourist driving to the town of Mediolanum contracting some disease then driving back to Germany and spreading it. You'll have a major catastrophe.
Historians and cultural anthropologists would all be clamoring to observe the Romans in their natural environment. Also imagine the reaction of 1.2 billion Roman Catholics around the world when they realize that Pope Innocent I is now their leader.