okay. I understand what your saying.

my personal reasoning is thus:

technically every rinnegan we see is artificial to a degree, at least to me point of view.
-Madara's is a replication of the original
-Kabuto's is a DNA one
-both rinne-sharingan and Six paths rinnegan are made from a tree made to absorb stuff from a planet for some purpose we don't yet know by an alien race. that big world tree is just a big energy harvesting tool to convert to a fruit.

it makes me suspect that the entire rinnegan/sharingan/byakugan thing is just highly advanced genetic and chakra manipulation that Otsutsuki made to do.....stuff. and that they're some alien civilization abusing less advanced races for their own ends whatever those are. there is no "natural" rinnegan, so whats the missing component to replicate the rinnegan in some lesser version? why can't the same chakra be produced again? what actually makes each one unique?

because at least the Mangekyo has a good reason why each one is unique: its based on the trauma and tragedy that you went through to get it. it in some relates to your own unique mental state.

I guess I just look at this very scientifically, so to me if there is a "false" and "True Rinnegan" it has to matter more than just being some minor detail. to me it says that the False Rinnegan isn't a failure, its just a work in progress missing some obscure component to produce the proper chakra even through logically it should not: after all, why is the sharingan and byakugan consistent with their abilities no matter how many generations pass, but not the Rinnegan? why do Indra/Asura have this shard of divinity nonsense, yet the the modern sharingan, byakguan and other bloodlines are sustainable? why didn't the rinnegan just pass on to both sons of Hagoromo? if the other bloodlines are components of the shard-chakra system, why aren't the current bloodlines breaking down and becoming weaker even further because of the limited kinds of chakra available?

it just raises more questions than answers to me, because False Rinnegan was ultimately superfluous to anything that happened, so I don't see why the author felt the need to include it. all the other bloodlines only need the genetics to work, why is rinnegan suddenly different that these other rules apply yet somehow led to bloodlines where they don't apply? what changed to allow the Sharingan to not divide like the rinnegan? why does the division occur at all? why does there need to be multiples of the same eye, with inconsistent effects? if each version is unique, why is it consistently unique? if Kimiko learns this kind of stuff, she'd have the same kind of questions and be just as driven to figure out why.

and the real answer which is "the author really wanted to emphasize how chosen by destiny Sasuke and Naruto is and how no one can ever replicate the rinnegan without being Madara, so screw everyone not Naruto and Sasuke I guess" isn't a good reason to me.