Ascians are immortal because they've already "died". Their original bodies are dead, however, their souls haven't finished dying by going to the Lifestream to be reincarnated later. To keep their souls from going the Lifestream, Asicans either possess dead bodies or hang out in the Rift, which they can only get to if they have Crystals of Darkness.

The entire point of Auracite is to put an Ascian soul somewhere it can't escape to another body or the Rift. All while someone is charging up aether to blast the Auractie with. I can't find any mention (even in the English version) that Ascian souls are really destroyed with this method either. What seems to be happening is that the aether blast is simulating the Lifestream. That is, it's surrounding an Asican soul (that should already be in the Lifestream) with so much aether the soul just... joins up with the aether. And then when the Auractie is destroyed and the aether blast dissipates back into the world, the Ascian soul goes with it. Instead of an Ascian soul joining up with the Lifestream, the Lifestream joins up with the Asican soul.

This would explain why the Thordan primal could absorb Lahabrea's soul and then Lahabrea is dead for good. Lahabrea is nothing more than a soul made out of aether... that doesn't have a firm tie to a body anymore. So Thordan can just absorb the aether of Lahabrea's soul like he absorbs all the other aether around him. And we know from other primals that what a primal is defeated, their aether is returned to the Lifestream. What we do with Auracite and the Blade of Light is... probably about the same thing Thordan did. We just are skipping the "kill off the primal" step and letting everything dissipate.

We actually do the "Blade of Light" thing even earlier to force Lahabrea's soul out of Thancred's body at the end of 2.0. But since Lahabrea isn't in an Auractie and has a Crystal of Darkness, he can escape to the Rift just fine there. He doesn't stick around long enough to be surrounded by so much aether he's overwhelmed by it. Bummer.

What does seem to be a reoccurring theme is that the aether of people's souls is somehow tied to the aether of their bodies. So long as their bodies exist, their soul doesn't seem to naturally want to go to the Lifestream. It's only once a body is truly dead that the soul wants to be in the Lifestream. So, I don't think what we do to kill the Ascians would really work on anyone else who is properly alive.

About Elidibus and Emet-Selch
Elidibus is the only one I'm not certain is in the Lifestream, because we see his aether (and the aether of all the Memorial Stones) be absorbed by the Crystal Tower and the Crystal Tower itself never gets destroyed to release the aether in it. The Tower can safely hold so much aether indefinitely that I can't see Elidibus breaking out either. The other thing that makes Elidibus different is that he's part of Zoidark, Zoidark's heart to be exact. I don't know if we really can return Eldiibus to the Lifestream until Zodiark himself is killed. So the Crystal Tower might just be a stop-gap solution until we're ready to defeat Zoidark for good.

Emet-Selch is weird, but not because of how we defeat him. We still flood him with all the Light Aether we picked up from the Lightwardens and also a lot of the Scions' donated aether. We just don't try containing him in an Auracite first like we do the other Ascians. Emet-Selch is weird because his own aether affinity is the aether of the Lifestream. (Check out his short-story from last year's Rising for more details.) He was quite literally the best Ancient at manipulating it. In fact, it's why he had the office of Emet-Selch to begin with. So when we killed Emet-Selch for real, we essentially sent him to the place his aether was already very, very skilled at manipulating. Which... could be interesting going forward. Or rather, has been interesting already most likely given who shows up when we use our Azem power to bring in someone who can pull us out of the Rift.

The Lifestream is where Hydaelyn also is. And we haven't been able to have contact with her since 3.4 when Minfillia left to save the 1st Shard. So it's high time we had a chat with Hydaelyn about all this... but how to get to her? I find it... very convenient... that someone who was really good at manipulating the Lifestream in life is now actually in the Lifestream. And we've already somehow called upon them once...