It would be logical to completely eschew characters if they didn't have such an enormous effect on the game. As it is, a monarch can completely define a nation's success, or failure - not to mention the psychological effect on the player. To have a fantastic 5/5/5 king be killed with an event that's basically, "Whoops, your king died" is the most galling thing to happen to someone. Introducing some sort of event chain for a death would be great.
As well as that, given the influence that Royal Marriages have over countries and dynasties, it would be great to have some kind of family tree, just in order to keep track of your royal marriages, and dynastic prospects. This is especially important for a country like Austria, or an OPM in the HRE, where getting Personal Unions and the like are extremely important for survival.
As well as this, how can monarch stats be pre-determined at birth? Surely they develop over time? I know that some people will think that this is too reminiscent of CK2's education system, but at the end of the day, a one year old boy is not going to be a better military administrator at birth than most people are at adulthood. Give us some way to improve a monarch's stats - make it punishing, but possible.
tldr; Characters, like it or not, have a huge impact on how you play, and where you plan to take your nation. We're not asking for them to be personal, just for our control over them to be more than 'Hey, your great ruler arbitrarily died', or 'Have fun with the rubbish ruler that just got born'.
Foul language removed - Seelmeister