The king did not truly desire the result of this path but the path itself. Nevertheless, this man wanted to walk this path, even if it meant that he would burn himself while doing so.
Avadil warned Arthur that the king was trying to go against life itself, and he was tolerating Arthur's offenses for the sole belief that he was a vessel. The king now got to confirm that Arthur was indeed a 'vessel.'
"I am afraid that I lack the knowledge to know which guardian you serve," said the king, probing. They were back in the same room they first started at, now with a different topic.
"I am not a vessel to a guardian," answered Arthur. As far as he was concerned, the legacy he had imposed no direct commands on him. Arthur still got to choose his path in the end.
There were legacy quests that appeared once in a while and warnings that Jizo sent. His current legacy quest was still the same, to prevent the key from falling into the Enders' hands.