How about having the first in line child (if there is one) take over?  It would make it more interesting.  I escaped being crushed by Magnar once because their sovereign was hurt and headed home straight past the city where my main force was...

Definitely agree with this.  Right now, lines of succession have almost no purpose that I can see.  Why even mention it in the game if it has no real impact on gameplay?

Not only should children take the crown upon the death of an AI's king, I want to be able to have my sov die and be replaced by an off-spring.  I just do not like this idea that player's sov are immortal.  It ruins an opportunity for some wonderful gameplay!  Having your initial custom sov die and be replaced by a child that has some but not all of your initial traits should make the mid to late gameplay suddenly change, refreshing the gameplay for the gamer as now he had to deal with an entirely different sov running his kingdom.  What is more, as Ilindil mentions, this could also unlock the possibility of civil war for the player, perhaps ruining his empire as it currently exists if not handled with care.

Lines of succession/dynasties, like tac combat, needs to be revisited and overhauled post haste to unleash its real potential for fun!