My vision for kings and such
Let me see if I can explain this well...
I think each country should have a "family tree" that one can view. This would show the current ruler, his ancestors, and his children as they are born. The default would be the historical characters, which would always be born and die on their historical dates, but there could also Be the option of having one or more random dynasties available per country, as well as the player being able to create and name his own ruler and children a la Genghis Khan. Their marriages and procreation and such would be done "under the hood" or perhaps based on the "royal marriages" diplo option (the two could be worked into one idea), and their existence would be important thusly:
every time a ruler dies (be it on a predetermined death date or random death date generated at the character's birth) an event pops up showing the family trees for all the powerful dynasties in the country and their members that would be eligible for the crown. Now, taking the historical heir (or the eldest son in the case of a ruling random or user-created dynasty) would give perhaps a stability bonus of +1 to simulate a smooth and expected transfer of power, which the AI would do 99.9 % of the time, but you could pick any candidate, and based on a number of factors (their "rank" on the succession ladder, their traits/abilities relative to those of the primary heir) would give a malus ranging from a stability hit (-1 to say -6) to widespread revolts to a civil war (where the country splits into two or more factions [eg England splits into England and Lancaster England when the Lancaster dynasty was running things But the player chose the York heir to be their new ruler... England would always be the player's country] with strengths based on the relative validity of the claims of the chosen heir and the primary, expected heir.)
This system would allow for both roleplaying and intrigue, and give more flavour to civil wars even when the player just wants to always go with the default historical leader a la EUII. It would also allow for assassinations of rulers and such to occur, although thay would of course have to be tough and expensive to accomplish.
So, anyhow, my vision is clear in MY head. If I haven't made it clear in yours, please tell me so and I'll explain better. I really do think a system similar to the one in CK only almost totally under the hood would be best for EUIII.