To get the trait Born in Purple you have to hold either the Byzantine Empire or the Restored Roman Empire.
However, you also need the cultural tradition Byzantine Traditions. The requirement of which is holding the Byzantine Empire. Once you create the Roman Empire it destroys all other empires.
The result of this is that you have only the window from gaining the Byzantine Empire to when you create Rome to establish that tradition, and if you don't you never can again.
I feel that is a little outside the spirit of the Born in Purple Trait since they allow you to be the holder of Rome or Byzantium. But the tradition required only allows youtto establish it as Byzantium.
Switching the tradition to be unlocked when you hold Byzantium or Rome would make more sense, since you can only restore Rome if you also hold Byzantium.
However, you also need the cultural tradition Byzantine Traditions. The requirement of which is holding the Byzantine Empire. Once you create the Roman Empire it destroys all other empires.
The result of this is that you have only the window from gaining the Byzantine Empire to when you create Rome to establish that tradition, and if you don't you never can again.
I feel that is a little outside the spirit of the Born in Purple Trait since they allow you to be the holder of Rome or Byzantium. But the tradition required only allows youtto establish it as Byzantium.
Switching the tradition to be unlocked when you hold Byzantium or Rome would make more sense, since you can only restore Rome if you also hold Byzantium.