Michael - You Asked.
Arithon and Lysaer both carry the "lineage" of Shand.
Note: the Fellowship sanctioned Arithon for RATHAIN.
Note further: in discussion with Maenalle, COTM, concerning Lysaer in jeopardy handling the Mistwraith, they KNOW that there are other s'Ilessid survivors on Dascen Elur.
If they know this, extrapolate, they are aware of other s'Ahelas descendents there, too.
Straight logic suggests that, knowing this, they'd prefer the bloodline untrammeled with the other royal birth talents of s'Ilessid and s'Ffalenn, given that the legacy left by Dari's descendents is already gifted to a more than prodigious degree…