I am curious what would be the best way to simulate things like this in game?
In CK2, a powerful duke or super duke may become the chancellor without actually having the highest diplomacy. May in fact be the lowest diplomacy. But it might be useful to hold him off because of the +15 point benefit, until somebody kills him or he dies in battle or somebody charges him with treason so he can be imprisoned.
Generally, if a game treats characters as tools that can be used in different ways, with a lot of simulated effects, there might turn out a situation that makes some unlikely scenario, useful and feasible. The meta game, not just the game itself or the rules in it. Humans will exploit any system for advantage or an edge, if they can see it. Sometimes due to short term profit, sometimes due to longer term strategic interests.
There's always that annoying character and rival you don't like, it would be so convenient if he got promoted and sent to the front lines, and accidentally ended up dead as a hero.
In Stellaris, perhaps some factional leader of some planet is getting uppity and starting to diverge from the mainbody, Culture. That leader is super competent, but if his sub species rebels, could be bad militarily.
I really like CK2's mentor and guardian education system. Really connects old generation to the new generation. It's a strong connection. I think instead of xp or random traits due to events, I would like to see that in any kind of Stellaris leader academy or manufacturer. Adds that personal touch often missing from random number generators, and since Stellaris leaders won't have interaction with each other, it'll be kind of hard to actually think of them as people... even simulated manpower. Since the POPs are the stars and they live on planets or something, perhaps a leader could become trained and educated by the POP and their culture itself. So a planet might become famous for producing war leaders or diplomats. Up until the AI rebellion takes them over and they become your worst enemy, at least.
Xcom original style management of manpower, personality quirks and traits, and various other issues of resource management that applies to the tactical battlefield, was fun and engaging. Also very tricky or creative at times. And it was all random number generator, but the skills improved directly in relation what that soldier did successfully in battle.
CK2 didn't have a lot of "upgrading" so to speak, in their characters. A lot of it was random or obscure or low probabilities. For a war leader, though, I think there should be some trait and event upgrades, that isn't a skill tree as in Diablo 2/3 for example. That's a little bit too orthodox. Instead of trying to make every game with leaders different, via low probability constant checks, they should give a really good trait to one leader, currently alive, and then decrease the chances after that. That way, you can play around with more interesting characters, given the 30 or so limit, without waiting for something to happen later on that may never happen.
The scientist leaders I think they will have a different and easier time balancing the career progression of. But military leaders are a little bit harder, because it's hard to predict how many fights or what kind of experience they can get, without the players doing weird things to them. In Ck2, that would be like teleporting 30 of your courtiers and council members to the army at the Crusade target, so that everyone becomes a crusader and loves each other. But there are other ways to "game" in game mechanics.