"The briar will take root on the day that Arithon s'Ffalenn embraces kingship."
Actually the Black Rose prophecy says nothing about Paravians, they are surviving just fine with the Fellowship as they are. If Arithon accepts kingship of any mortal enclave, the compact continues and the Paravians return. That would also need enough of the clans to suvive in order to uphold their part in maintaining the free wilds. Arithon's talents are probably better used elsewhere. And keeping the clans isolated from the townspeople has not worked out that well. Paravian survival when the strands were cast was not dependent on Arithon accepting kingship. The Fellowship were willing to release Arithon from kingship before they heard that Black Rose prophecy. Arithon assumed their survival was dependent on him accepting kingship, the Asandir let him think that.
If you read back through the bits concerning Daviens reasons for what he did, the rebellion, and what Arithon and Davien both want, you will see Davien never intended Arithon to accept kingship of Rathain, he has something else in mind. There were problems with the compact that have been mentioned in the books, it is basically unstable since it is widening the differences between the clans and the townspeople, creating two groups with completely different ideas of what should and should not be done with Athera. The Fellowship knew there was a strong chance humanity would eventually break the compact. Davien was working on an alternative solution. King Kamridian died, and Davien stirs up a rebellion to topple the kingships, maybe kingship was the reason why Kamridian failed.
The Black Rose prophecy says when Arithon is willing to
embrace kingship, says nothing about him actually needing to be crowned for the Fellowship to be reunited. Twice so far Arithon has agreed to accept kingship, twice something has happened to prevent it, something is likely to be appearing out of thin air when Arithon volunteers again after things have settled down.
And Davien's words on the matter were.
To marry you with wisdom, you would have to be inflamed until you mastered your rebellion.
If you look at how Arithons's talents have been developing, and that Davien probably wants his freedom from that compact. It seems likely Arithon will be taking over the earthlink from Sethvir. Although Athera might not be the wisdom in that quote. But by the end of Destiny's Conflict Arithon would have mastered his rebellion, maybe accepting guardianship of Athera and the earth link is what Davien is refering to, maybe that is the alternate plan. He marries part of Athera by accepting kingship of Rathain, what does he get if he accepts the earth link?
The mighty endowment of vision he possessed had been ceded by the last Paravian. Its tied power married Sethvir's awareness to all that transpired in the world. Few could have endured that grand flux without losing their minds to insanity. Sethvir had done more, had embraced and encompassed the whole by surrendering every aspect of his being to address the needs of Athera.
Of course I could be wrong, but who else can take over the earth link if the Fellowship are freed and decide to leave Athera? Arithon has a bit more to do before he is ready, but tackling that mistwraith in Rockfell should go a long way to achieving it.
Which brings us back to the original point. If Arithon as a sanctioned crown prince is still tied to Rathain, does that affect things. As a royal trying to avoid kingship, does he need to be freed of that destiny before he dies. Or does dying free him of it? Even if he could get the rest of the attunements, without Fellowship help, he has no blood inheritance for Havish or Tysan. Now there might be some strange tie to Lysaer we have not unraveled. Tarens might be a missing link. And Elaira could be headed for an impressionable encounter with the coronation of Havish's queen. But none of that seems likely to help if Arithon needs something to change before he dies and wanders off where ever he is going.