I am not disagreeing on if ruler/leaders are different entities.
I am of the opinion that you can make leaders immortal work to benefit of getting people to want to play Hive Mind by making them unique in that they get immortal leaders from the beginning. It doesn't hurt that it flow well with lore for immortal ruler.
No they are NOT suffering from multiple personality disorder. There is same personality running on many immotile in different clusters, best working in-real-life example is distributed computing aka cloud computing, and many personality within a mind disorder. They are not even remotely related to each other.
To expand a bit on distribute computing; A very huge complex problem that will take "forever" to solve is break into smaller chunk and given out to different computers to solve and combine the result together to form a solution.
The key word is to delegate some smaller tasks to drones who can take care of it themselves. In the same way Queen for ant or bee doesn't go outside and gather food for the entire colony by itself.
I can see you are still having trouble conceptualizing what I am saying. So I will try a more simpler example. Suppose if you are capable of copying an entire memory/conscience everything down to the last quantum state and carry transfer/update over to a clone many time over.
So instead of trying to have a single clone hover parent over a trillions of same clone. Even if you tried to you would never get anything done!
You would have one original or oldest clone or whatsoever at the top making high level decisions. Then you delegate lower level to another group of clones (empire to planet to state to city to councilor etc...). Repeat until you reach the bottom of the chain lowest task that can't be delegate any further more.
Now take that example and throw in PSI or cyber implant or pheromone (doesn't really matter how you ties all those conscience into one that much) then you have a Hive Mind that has autonomous drones and ruler that are immortal.
Hive Mind is a single entity.
Theoretically speaking, a ruler might not even be immortal in the flesh, unless the ruler himself is the hive mind entity itself. If not, a ruler is merely one of the drones picked by the hive mind to "represent" the empire. But it is highly unlikely the drone species (including the ruler and the leader) are immortals, only hive mind is. Because hive mind can be removed and if they become normal species like the non-hive mind species, they would age and die off. In any case, it's most likely the drones are not immortal. And this includes the ruler. So there's one reason why leaders shouldn't be immortal.
If you put the so called "distributed computing" in terms of government, that's very decentralized, which is the total opposite of hive mind. It's very simple to understand hive mind. Just think of one entity within bodies of multiple, and they move as one. But hive mind is "omnipotent" enough to make sure not everyone gets mobilized when they aren't supposed to, I would guess. However, compartmentalized governing is not hive mind. That's a major flaw, if that's "hive mind". But I am sure the hive mind forms some kind of "departments" with its drones, to complete many different tasks, just as we human beings have hands, feet, and fingers. Still, even so, Hive Mind is still a one entity. Therefore, one ruler, one ideology (or what ever it's capable of in terms of leader bonuses).
I am not going to talk about "clones" because cloning and hive mind are two different things, and the game doesn't have cloning leaders at all.
Hive mind is a single entity, it resides within everybody under its influence, including the general POP, leaders, and rulers. So they are all technically one. Delegation doesn't exist, because they are ONE ENTITY, CONSCIOUSLY.
"Empire to planet to state to city to councilor" is typical structure of conventional government. That's pretty much how most decentralized/federated governments function... Hive Mind is a single entity, there is no need to delegate to "lower levels" because there IS NO LOWER LEVEL.
The devs definition of "autonomy" is quite vague. But in any case, it's clear enough that all drones are one entity within the hive mind, and leaders would have autonomy to certain extent to have their abilities to lead fleets, oversee sectors, and do research. Autonomy is given by the hive mind, but where these leaders get the ability from is not so much a mystery, because like I said before, hive mind can be removed. So these "drones" are clearly capable of self-consciousness, but are bound to the hive mind entity in some way. Therefore, I would assume, while hive mind may grant autonomy, it might also be unlocking the "potential" of the drones. In any case, the drones don't receive consciousness of who they are and what they can do, by the hive mind - because that part of their consciousness already resides within them, so to speak. It is merely (not granted) unlocked by the hive mind. That's only done to RULERS, of whom the hive mind have direct control over. And to have these leader abilities, one must have characteristics. And drones (the hive mind itself) does not have characteristics so long as they are under the influence of the hive mind. Autonomy could mean that they are able to have these characteristics, in order for them to have these abilities.. (An example of a characteristic would be "unyielding", which some admirals get)
Transferring consciousness of an individual is not hive mind's job. Hive mind's job is transferring ITS own consciousness upon everybody else. So no. No immortal leaders. It wouldn't make much sense anyways, because drones are not immortals, and leaders are drawn from the pool of the drone species. Just because you apply the hive mind trait to some species doesn't make them immortal. Neither will their consciousness be immortalized. Only the hive mind consciousness is immortal.