The quote is in my reply to Cannoli.

And your point about Tamra not opposing Elaida's posting is invalid. Of course Elaida's relationship with Morghase played a part. That's one of the things Elaida brought to the table as a candidate.

The BWB also makes clear that both Hawkwin and Ishara got advisors, who they accepted.

How do you propose your way works anyway? Do the rulers come to Tar Valon and inspect a line of sisters? Do sisters compete to gain the favor of the rulers? It makes no sense.

Obviously, what Elaida did with Memara and Duhara (thrusting an advisor on a ruler), isn't done either. The rulers have some say. They can probably send back advisors they're displeased with (as Morghase and Hawkwing did). But there's also no doubt the Hall has a say in who is chosen.