The first and obvious answer is that they were, at one point, dead. Even if their return is a known thing, they died and anything tied to their living form has registered that.
The first noble/monarch to do this to themselves did not arrange for a change in the laws to maintain their power after death, either through accidental or intentional action. The living heir, now ruler, does not want to give up the power to their unliving parent and so they do not arrange for the laws to be changed for them.
Fast forward through the generations, and now it is an ingrained custom for the deceased noble to step aside allow their living heirs to take their place. They still enjoy relative prestige and influence by being a entity of great experience without the responsibility of actually running the show, while also allowing them to pursue whatever ignites their interests.
This assumes, that they were/are good sources of wisdom.
But that's a bit boring, and assumes that it is all benevolent. They are undead aristocrats and businessmen … I doubt "benevolent" is in their vocabulary. This leads to the follow-ups …
Game Behind the Thrones
Of course there are people(?) that want to rule after their death and subsequent rebirth. Unless this is one world-spanning kingdom, it is likely that there are various degrees of success throughout this world and likewise many ways that it was prevented from happening.
An advisor of much influence can rule without ruling by the expedient measure of being the single most trusted advisor to the ruling line. But once you get enough of them around, it is plausible that they will turn their ambitions on each other and attempt to deal with their own cohort so that they are the one true advisor to the leaders. The cunning survive and thrive, while less apt suffer for their failures.
Basically, they play a deadly game behind the scenes that lays mostly out of public view. On occasion their experiences are tapped for advice.
Basically, an Undead version of Game of Thrones only with the R-rated stuff converted to more verbal warfare.
Ambitions of the Ghost Council
A second scenario is that they do rule, just not on paper. A shadow cabal of immortal undead keep a watch on the world, nudging events in the directions that they want through advising the leaders of the world.
However, this shadow council also has a secondary function of watching over their own to ensure that the political balance of the world is maintained. They are the ones to keep the rogue elements of their cohort neutralized through their own machinations.
This situation could arise both based on groups of any motivation, and even have multiple cabals with conflicting goals that have entire shadow wars, or manipulate events into real wars. A layer of politics under the politics that might make for an interesting intrigue setting.
In short, they are too busy allying with and scheming against each other to really achieve global rule like they used to when they were alive.