As I wrote before, I noticed a strange comportment about pontifical election: during all my games, the new elected Pope was each times a random young man and not an experienced cleric chosen from existing characters. Recently, one of the elected popes was even a inbred idiot! Moreover, several of these characters weren't very religious (they generated bastards)... It's not the Gregorian Reform at all, it's the return of the Pornocracy or the Borgia Era in advance!
I said earlier, that it is particulary illogical considering the period in which the game action occurs : the Election Reform was created by Nicolas II in 1059 and the Gregorian Reform is coming soon after.
Moreover, the original database contains a lot of characters which are really more accurate to be righteously elected (for example, beginning near 1066, Hildebrand, the famous Gregory VII and actual successor of Alexander II) and the later database (during the game) will contain enough bishops and chaplains who may have the experience and the piety needed to be elected to the papacy.
With this system, any existing character can't access to the papal throne: starting in 1066, neither Hildebrand (Gregory VII) or Odo of Burgundy (Urban II) will be popes. And as the mechanism is implemented during the whole game, there is no chance that a character from an existing dynasty (hence, from the dynasty of the player) can be elected as the legitime Pope (I don't refer to the anti-pope feature here).
While the new system of investitures seems a very important step for gaming immersion, the mechanism of the papal election seems a rather unfortunate regression (I even think that the system used by CK1 was finally better).
I don't know if implementing the College of Cardinals (as some people have suggested on the forum) would be the solution (it would probably be the best feature, but complex to implement). But already, configure the papal election from existing characters (and not new random characters), including choosing a pious and unmarried (or widowed) character would be a good start.