Leaders getting negative traits out of random is not internal politics. It is salt, not main dish. Main dish is something like:
I'm pacifist, materialist and xenophile empire. I need to select new governor for Abacus Sector. There are three candidates.
Abacus Sector is populated mostly by Spiritualists, because some Holy Artifact of Holiness I found there by accident generate big Spiritualists Attraction for whole sector. I have Spiritualist candidate in rooster, and putting him in charge of Abacus will make local POPs happier on average, which will have positive impact on Stability and therefore production efficiency. On the other hand, he will increase Spiritualist Attraction in sector even more, and his nomination will make Spiritualist Faction stronger in parliament.
Counter-candidate is materialist with industrialist trait, While boost to factories production will not matter much in mostly rural Abacus, he is skilled, so will reduce Spiritualist Attraction while not decreasing stability that much.
Third candidate is an idiot of Militaristic Faction. I would never consider giving him responsibility for anything more complex than pencil, but I played roughly wit Militarists for some time, their loyalty is deep in red, and they are one negative event from starting Rebellion Progress. Rebellion Progress, while almost surely will not result in rebellion (it is called Progress for a reason...), can generate additional hard to foresee negative events. By placating some colonel idiot son, I can brush off this problem.
There is also fourth solution. When I established Abacus Sector, my sector size was limited to 2 star systems from seat of power. Current-day technology increased than number to 4 star systems. By dissolving Abacus and dividing its territory between neighboring sectors, I can dilute HAoH influence over more planets, therefore making it weaker and ensure that Spiritualists will not get majority of votes in any of sectors, therefore decreasing their influence in parliament. It would cost me influence/unity, though.