Are shards different?

[Rulakir]

The other way you could hodgepodge this all together would be if there was a kinda 'tipping point' where once both the body and soul were fully Rejoined, they would go "Oh wait! I remember what I'm supposed to be!" and snap all the way back to Ancient-hood all at once, like finishing assembling a broken machine. So just having an Unsundered soul in the Sundered world wouldn't be enough.

This is implied via dialog from Alisaie in ShB: "The starshower didn't awaken me to Hydaelyn's voice. But that vision of the Final Days, of Amaurot burning... It filled me with sadness to the very pit of my being. Things I once knew, people I once loved, promises I once made... It felt as though long-forgotten memories were dancing at the edges of my mind. But when I try to focus on them, they simply fade away. An effect of having a fractured soul, I shouldn't doubt."

I believe the idea was once the Source was rejoined the Ancients would regain themselves. Not to mention sacrificing rejoined Ancients is counterproductive to their goal as we know their souls would become trapped within Zodiark.

Edit: It's possible the Ancients were deriving their power directly from the star somehow, so even if their souls are whole as long as the star remains sundered they'll be unable to return to their previous Ancient form.