The Reasoning behind The Sundering? (*6.0 Endwalker Spoilers*)

[Kordarion]

If they wanted to be, yes! <--- The keywords in what you quoted.

If an ancient has to become a primal, merge themselves with a mythic beast or cheat death by going to an in-between world when they should be returning to the aetherial sea to become immortal it doesn't mean they are naturally immortal. If a modern human found a way to become immortal that only affected themselves you wouldn't go around saying that all modern humans are immortal would you? To be fair whatever it is that the unsundered did to return after death could be something inherent to all ancients but as far as I am aware there is nothing that says it is.

Also you are sort of right when you say they don't die when their physical bodies do. As evident by Emet, Hythlodaeus and sundered like Livia, Ilberd, Minfillia and others when people in FF14 die they do remain themselves in the aetherial sea for a time, but evidently they don't permanently remain the same person in the aetherial sea as otherwise every character we meet would be able remember their past lives and the sundering memory loss wouldn't matter after a generation. Not to mention their are real world religions where when you die you still exist as yourself in the afterlife so that doesn't mean existence after death means you never died.