and also the emperor being forced to impregnate women one after the other and not being able to have one woman until the trait appears
But isn't it the same in real life, where especially nobles and royals were forced to produce a lot of kids until the desired son was born?
Like Henry VIII marrying 6 times, because he needed a legal born son.
Or the last tsar of Russia having 4 healthy daughters until finally a sickly son was born.
does it make it any more tolerable to know that even in reality there is children who can be hated due to genetics(in this case gender)? What I focus on is the fact that in this fictional story the children face hate either for having or not having something they can't control. If you expand to the remarriage and the objectification of women for pregnancy, and then its how the mothers in this story had so much hate internally and externally for not giving birth to the special one it twists their love for their own children and pushes them to act out maliciously towards innocent children. The mid way as a reader would be to recognize the system they are in, but for morality you probably should not forgive as a child's life was in danger.
You can apply the example of remarriage to normal families too, especially in cultures that favor men. Then you reach points where someone who either married for love or an arrangement will be told by those around them(usually bio-family) how they are useless for not having enough children and enough males. With the men probably being placed as a victim, or pushed toward divorce so that he could finally have a real son. Heck you can go listen to stories in such cultures how cheating husbands bring back children and extended families may push for acceptance and even for the wife to raise the child based on the fact that it's a boy.
In the story for emperors who have harem, then they just keep taking in people and while some can seek power for their bloodline it often is based on fertility or beauty. Therefore for this story I will pity the children as politcal games of marriage and the possible benefits it brings doesn't always apply to them.
I never said it is okay, but it is a fact, that powerful families often have several children in attempt to produce the desired heir. And it is always shit for all the spare children, not being chosen because they are not the firstborn, no boy, not the most intelligent child or not the most gifted in any other way.
But the concept of treating and loving all your children equally is quite young and similar to treating men and women equal needs still a lot of effort to become reality.
All of them were basically born soley for a single genetic trait. Constantly pumping out kids until one matches, and with the way its implied urgently its the way it has always been too. Then each and every kid before would then be subjected to disdain of some kind by the adults around them for not having the special genetic trait.