Since the rings were buried with Cozart’s body and the knowledge was hidden away from his descendants, I believed that Cozart intended to be the first and last Shimon Boss. Since its odd if he intended differently, because Cozart’s family and Enma’s family were the only two families to use the rings. And Enma’s family found it after the earthquake revealed the rings to Enma and his family.
I also say that he had a pact with his guardians that when he died the rings were to buried with him. It was a secret that died with the Guardians.