As it stands, political succession is a bit too much of a painless process -- you might lose some good perks, have to spend some influence, or have a new mandate to deal with, but then it's pretty much business as usual. I generally like their choice in Stellaris to progress further away from rulers and individuals being a game focus, moving towards broad government policy and administration of an interplanetary empire, but the game could use some real political leadership crises. It would be especially helpful for potential destabilization of overly powerful empires -- if a player doesn't keep some influence or resources banked at succession time, things could go bad.
It could also be a way to keep the AFE steamroller from going out of control -- if they could split and have internal disputes during succession, it would give you and standard AI a chance to respond (although those splits probably shouldn't happen during the War in Heaven, as it would be the unified war between two awakened empires dedicated to each others' destruction).