Here's one of the technical points which I think highlights a problem with the show.
The whole genetic dynasty thing is based upon a basic knowledge of biology that twins tend to do similar things and thus, are the same person with a few superficial differences. And sure, given the fact that they live together and occasionally wear each other's clothes, etc, one could make that case.
So now, the fate of the entire galaxy is based upon cloning and maintaining a type of identical Cleon to provide the face of eternity. Well, if one has 400+ years to work with, will that person have a 40 to 70 year old mentality forever? I would think that a healthy, non-bed ridden person, even at the age of 90, will try something new even if he's in his final decade of life.
This then brings up the whole contrasting Avatar thing. Hari's death by Raych was really his birth in cyberspace. Instead of a frail 60-something, he's now immortal and can pursue research till the end of time or at least till the end of computing machines. And yes, the show does appear to make this the case so that the time vault is actually a Hari-personality AI.
Likewise, even if Cleon used a type of body double occasionally, his consciousness and memories from prior lives would be assimilated into them, given the tech of his century. In addition, even if he didn't use direct clones, couldn't he grow organs and have his surgeons swap out aging ones and thus, extend his human life in the hundreds of years? The show has indicated that we're 1000s of years in the future where all of this exists.
Instead, we have a type of inconsistent universe building of medievalism mixed with tech, way ahead of the era of Genghis Khan. Gaal's home world would be the laughing stock of the galaxy, as ppl on Trantor and other planets would take bets on when the deluge happens, since it's obvious that the idiots on the surface aren't doing anything about it. And one could say something about Lumin being another Luddite, anti-tech, fake Buddhist world/culture but that's for another day, since earth's own Buddhism allows for soul to transmigrate/live anywhere. I mean sure, ppl love to visit medieval places like Bhutan or Tibet but on the whole, modern practitioners of the faith live in places like Thailand, Malaysia/Singapore, Sri Lanka, Europe, and America.
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You are assuming that a personality AI is better than a live human being. I think it's an inferior version to a live human being, and the argument between Raych and Hari Seldon just before Raych killed Hari may have been an indication of that (maybe his brain was being taken over by the AI, and his reactions were no longer quite like Hari). If AIs are inferior, the genetic dynasty makes sense. And Hari Seldon probably didn't want to make a clone of himself, on the grounds that he didn't want to start another genetic dynasty.
With inferior AIs, it also makes sense that a copy of Cleon with downloaded memories is used only for emergency replacement, and not as the usual method of continuing the dynasty.
There is no reason to think that swapping organs is a viable method to extend life much longer than the normal human lifespan. It may not be possible to reverse brain aging, in which case, swapping organs would be pointless.
It's reasonable to assume that interstellar trade happens at a rather low rate, since there is only so much stuff that can be worth transporting between stars. So having wildly varying tech levels between planets is quite understandable, assuming that each planet has different levels of different resources. It does nobody any good to have information, if your planet doesn't have the stuff you need to implement the knowledge. Besides, in the case of Synnax, it seems that something went pretty awry with their religion.