"Transcending the flesh" is a euphemism for dying. Or at least, the first requirement of death in the FFXIV world; that is, a souls becoming separate from its material body. The second part of death is when the soul goes back to the Aetheria Sea/the Lifestream. The Ascians and the WoD (and anyone else who would travel between Shards) would not do the second part. Preventing the second part is probably impossible if the soul in question does not have the Echo.

The Scions have not "transcended the flesh" as their bodies are still attached to their souls and are sill properly alive. Their souls just aren't in their bodies at the moment. Which suggests they are still on the Source. What is very weird is that their souls are not anywhere souls usually are (lost in the Aetherial Sea like when Y'shtola used Flow, or something of that nature). There's also the fact that the Scions do not have the Echo, so even if they were to "transcend the flesh" their souls would probably do what everyone else's souls do when they die and just go back to the Aetherial Sea and be turned back into raw aether. That is what Krile was looking for with Matoya's Crystal Eye in 4.5 Part 1 and found that the Scions souls had not dissipated into aether; they'd "simply" somehow left the Aetherial Sea.