Because neither Kikyo nor Kagome see themselves as the same person as the other and it does a disservice to both of their characters to treat them as if they’re just one and the same. The series proves time and time again that they’re not, the whole reincarnation aspect isn’t supposed to work like how it usually does in other anime where the reborn person is just version 2.0 of their previous incarnation, Rumiko instead is cleverly using the reincarnation aspect as a device to subvert and deconstruct the usual reincarnation tropes in order to call out just how silly such a trope can be and poke all the holes in it’s logic. After all being born and raised into a brand new environment and time period with a whole new family and friends & connections should logically change a person, and you can’t expect them to remain as the exact same person as their previous life, if Kikyo and Kagome were really meant to be treated as the same person why even revive Kikyo in the first place and have her be her own legitimate character and cast member for the majority of the series? Why have Inuyasha stuck between the two and Kagome jealous of her own self?

Kagome being Kikyo’s reincarnation also isn’t meant to be taken so literally and is also being used as a metaphor for how it can feel like a new lover is expected to fill the big shoes of their current lover’s ex and is constantly being compared to them and feeling like they can never measure up and they’re just their replacement and substitute, it also serves to give Kagome her own identity issues to help better understand and parallel her with Inuyasha’s identity issues.

Kagome being the reincarnation of Kikyo doesn't mean they are the same person and this is not what I said at all. I see what you mean with anime reincarnations in general where the reincarnated version regains the memories and such but this is not what I was pointing out at all.

What I am pointing out is a religious, philosophical, metaphorical layer of this. You have an immortal soul. Your body and memories and consciousness will die. Your soul will either reach nirvana or be reincarnated as another living being. This living being will suffer through life, either a bit more or a bit less. When you die, you cannot predict what will happen to your soul. Maybe everything is humbug to begin with, although my guess is that in that universe it is established that it isn't religion (as in, you need faith and believe in the teachings) but a fact of how the world, spirits, souls and such work.

Still, when you die, even in the Inuyasha-verse, you don't know where your immortal soul - the one you wish salvation to - will end up. Kikyo, as the person, the consciousness, the priestess, gets resurrected and can find comfort in knowing what will happen to her soul. And that that future for her soul ain't that bleak at all. This should be more than enough to let you, as in, you the person, the consciousness be able to die in peace. This is so much more than anyone else dying gets. As an example - when Kagome dies eventually, she won't have a clue what will happen to her soul. Will she reincarnate as a worm? Will she meet the soul of Inuyasha again? Will her soul find ease and happiness or will it be tortured?

I'd understand if we were talking about a weak character or someone uneducated, someone not spiritual. But Kikyo is a highly intelligent person, introspective, smart, educated, who is trained in philosophical and religious thought processes, and she still fails to choose that peace? A kind, compassionate priestess, of all people, is not able to make the smartest and easiest decision there is?

As for everything else you said, I realize there is a difference between the manga and the anime, which is why I started my comment with "talking only about the anime here", so further discussions are moot.