Thirteen's sickness was from over exhaustion, so if he wanted to get better, all he had to do was obediently rest.
Metatron could have healed him with his powers, and Tristan could have given him the most potent medicine the military had developed.
But neither of them did that.
Metatron knew that if he helped Thirteen recover right away, he would once again tinker with projects that would potentially result in him getting sick again.
After confirming that Zion's life wasn't in any danger and that he just needed to rest, Tristan also refrained from helping his son-in-law recover as fast as possible. It was in everyone's best interest that Zion properly rested and stayed in the safety of Casimir City, not running to dangerous places.
Both only wanted what was best for the young man, even if it meant the young man felt discomfort for a longer time.
Thirteen wasn't stupid and also understood this concept.
