This was a continuous problem for the Romans. You'd think that they would have learned with the continued dynastic success of the Heraclians expanding the Empire beyond Justinian's borders. This problem was what doomed them after Manizikert with the various pretenders inviting the Turks into Anatolia to help them take the throne. This only caused the loss of Anatolia. Once the dynastic stability of the Komnenoi in the 11th and 12th centuries was lost, the state floundered under incompetent leadership with shaky legitimacy. If Justinian succeeds the Romans will for the first time have a dynasty last for five generations. Perhaps he can transition the state to gradually recognize the blood of Heraclius as the only true legitimate royal line for the their throne. With Heraclius's achievements' his dynasty should be seen as a second Constantinian dynasty.