That makes great sense as well. To keep beating the Roman analogy to death, the Eastern Roman Empire did clash with the remains of the Western empire, trying to take it back under the Roman umbrella (Justinian/Belisarius/etc). They sent armies all over Italy/Spain/Africa/etc trying to re-unify the old Empire. It didn’t work, since the new kingdoms that emerged didn’t want to be under the control of the far-off emperors. Once they split, there was no going back to unification.