That empire isn't going to last long anyway. Apparently all it does is use the stick, without knowing how to use the carrot. The young bastard daughter of the defeated king could be used for propaganda purposes to make the empire's rule over the conquered land more legitimate. Instead, the emperor and his people can only think of killing her, either immediately or when she turns 18. Considering how she was treated by her family, it's doubtful any lingering nobles could use her for anything much in a rebellion. What would they say? "The empire is so evil they didn't execute this little kid! They must be brought down!"