Theoretically, killing Miss Christen over her actions was way overboard as a punishment.
First of all, Miss Christen didn't nor tried to kill anyone. She was nothing more than a superior spy since ordinary ones could easily fail to spot what was happening on Baoway. After all, its leader was an evolved warrior, so only an evolved warrior could match him.
Moreover, Miss Christen wasn't to blame. She was following the Excellencies' orders, making her nothing more than a tool of the real culprits. The fault was with the Nognes family, so the punishment theoretically had to fall on it.
Also, evolved warriors were powerhouses and critical assets in the Global Army's upper echelon. Killing one of them could shift the frail power balance in many directions. In this case, it would weaken the Nognes family, consequently affecting Khan and his relationship with other nobles.