I add this:
- Make usable the so called Papal Succession for secular rulers too. For example it could be used to mimic the Roman Senate that should elect the ruler of the Roman Empire and the Electors of the HRE (after the golden bull). Some way to have more clear why the Preferatus (Caesar / King of the Romans) is... preferred. I suppose some mechanic to try to convince with bribe or whatever to vote your Preferatus should be necessary for be usable for player... in the end it seems always a random bishop is selected with no particular interesting trait (a learning 5 bishop become the Pope and my chaplain with 25 no? Why?)!
- Appointment Succession for indipendent rulers this should mean that effectively you have the power to select your successor without having to bribe anyone... this could emulate the Late Roman Empire and probably Byzantium itself...