Letter from the Final Emperor

The Final Emperor knew he was leaving a constitutional crisis behind him. There was no heir. At least, not one that all the families would agree on. Although his family had the greatest power to control the Crystals it came at the cost of difficulty conceiving. This meant there was a shortage of cousins and distant family members to pass the throne to.

Succession requirements

He knew the families would compete over who would follow him, so he set a series of conditions for his successor to achieve in order to claim the throne.

1. meld with the Radiant Phoenix and gain a feather
2. receive a crystal from each family
3. combine these crystals into their crown

He hoped that the combination of these tasks would assure the next emperor would have the support of all the families, and the protection of the phoenix, as well as being a strong crystal user to be able to meld them together.
These requirements were shared with the Advisory Council of the time, and the Archivist ensured they were followed. No one was able to fulfil these, in part as they all refused to support candidates from the other families. And because none of them were able to get close enough to the phoenix to bond, and were instead attacked by the bird. Which is why the Parent Council was formed and took over leading the empire.

The hidden guidance

Unknown to anyone else, the final emperor wrote instructions to help with the first of these tasks. These took the form of a letter to his friend, the archivist. His knowledge of the phoenix was unmatched as he had studied what his predecessors had left behind about their bond with the creature, as well as being able to study his own phoenix.
He left this letter in the solar of his palace, assuming the Archivist would find it and use that to guide who he thought was a sensible candidate. But the archivist never returned to the solar after the Final Emperor's passing. So he never received the letter and was unable to advise any of those who vied for the throne.