Damn, I missed the dev diary, but I hope the devs still read this. (I haven't watched the stream,yet , to be clear.)
I definitely support the idea that any court members can die at any moment, be it of old age or in battle etc.. But loosing a marshal to the flu and then your formerly highly skilled army turns into a bunch of amateurs, because their skilled leader is no more, is a terrible thing. It might also take a long time to get it up again. Therefore, I would like to see a mechanic that allows to prepare for this moment. Like to have a semi-skilled character available to replace the recently demised one. There was the idea of the son of the lord replacing the lord and inherit some of the skills. That would be one option. I would suggest that at after the first lord/court member reaches a certain level, he can take on an apprentice that costs a little bit of upkeep (he needs to be fed), but does not give any bonuses to the court member or his actions, but can replace him in case of death and inherit some of the skills or start at a higher skill level according to the time he spent as an apprentice and his masters skill level. Or he could also gain some bonuses over time that buffs his master and later himself. That way, a loss of an court member does not provide too great frustration. And the fact that you, as a player, will have to assign the apprentice (or son) by yourself gives you options. If you don't assign the apprentice you save some upkeep and if your court member dies you start at 0. Also, if your army gets wiped out completely, you should also start at 0, because your apprentice is most likely killed as well.
Another thing I was wondering about: What about traits? Like, a certain character performs a certain action a certain amount of times, so he gets a constant buff to this action regardless of his skills. Or he gets some follower which buffs the character. The apprentice could be one of them and he could inherit them ones his master dies. Traits can be applied to units in an army, as well. So, if the marshal dies the army has still some buffs that makes them not to become amateurs again (even if he next marshal starts at 0).
I don't like the option to just pay a large amount of money to make the character more skilled. No one gets better in anything just because of money. The availability of education however could influence the starting level of characters. For example, having universities in your kingdom raises the starting level by 1 for each university (or any other number).
Sorry for the lengthy text. I was just brainstorming a little bit. 😉 But especially late game, loosing a skilled character and replace him with a total noob is just frustrating. In a well developed kingdom, the player should have the option to start with a semi-skilled character to replace another one in the mid to late game. I just put down some ideas which could be implemented in many ways and combined the way you like.