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They all react like that because childless queens/consorts/etc were super easy prey and completely powerless in a royal court, no matter whether the royal marriage system was a monogamy or a poligamy: the only way for them to get any agency in the palace, let alone the power to protect themsleves, was through acquiring the "title" of mother of one of the king's potential heirs...
There are even stories where childless queens/consorts got so desperate to get out of that completely powerless "easy prey" status that they resorted to ANY method, from stealing babies and passing as their own, to getting pregnant by some guy related to the king (so the child, while illegitimate, would still get a chance to look like the king, somewhat) or even adopting (this last one, in Chinese royal harem novels)
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And, make no mistake: by "powerless" I mean their very lives could be in danger (as powerful nobles wanting their daughters to steal their spot beside the king might have even resorted to scheming their murder... something they wouldn't do if the queen had a child, simply because that method would be rendered useless, as they'd now need to get rid of her *child* first, before anything else, something a lot harder to do because royal heirs were a lot more tightly protected, with their mothers getting better protection too along with them, provided they *survived* giving birth)
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You can read chapter 89 of "I Am Trying to Divorce My Villainous Husband, but We Have a Child": the crown princes sent soliders who almost got people killed while trying to get their hands on to catch her husband's (the crown prince's) illegitimate young son, and snatch him away from his foster caregivers, so that they could bring him to her she could adopt him herself, to use him as a tool to keep her own position from being snatched away by her prince husband's mistress.
https://www.mangago.zone/read-manga/i_am_trying_to_divorce_my_villainous_husband_but_we_have_a_child/uu/nml_chapter-89/pg-1/
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In a previous chapter, chapter 86 of the same story, it had been established the crown princess (crown prince's wife) did all this because she thought it was the only way to stop the scheming of her mother-in-law (the queen), who she now knew was plotting to get rid of he, so she could bring in her son's mistress, and get a grandchild and royal heir from the son's mistress:
https://www.mangago.zone/read-manga/i_am_trying_to_divorce_my_villainous_husband_but_we_have_a_child/uu/nml_chapter-86/pg-1/
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Then there¿s chapter 15 of "I Will Fall With the Emperor": the emperor basically offers to the mc, who is his empress in name only, to get her pregnant to secure her position, and that this and his favor will induce him to protect her and help her live "well" in his palace (which, in the context of this story namely means, "safe" from the schemes of the other royal concubines, who, if you read that story, will notice were quite the *murderous* bunch).
https://www.mangago.zone/read-manga/i_will_fall_with_the_emperor/uu/mk_chapter-15/pg-1/
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If you want non-manhwa examples: There's "The other Boleyn girl" (about Henry VIII and his six wives, which is basically a trope namer) and a chinese example in the "The princess Wei Yang" chinese web novel, where you got a super nasty imperial harem (but I'm saying this just about the web novel, and not its TV series adaptation, bc they changed EVERYTHING there)
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You're welcome. I even found another example in a brand new manhwa, chapter 2 of "My Wish is Two Separate Beds": The Queen tells the Crown Prince's wife that she must have an heir to protect her position (both hers and her husband's) and that almost anything is preferable to remaining childless, even the off-chance of finding a "trusted" female friend to do her the "favor" of becoming her husband's concubine and bearing his child for her, *without* coveting her own position as the main wive and official queen.
https://www.mangago.zone/read-manga/my_wish_is_two_separate_beds/uu/to_chapter-2/pg-1/
i have mixed feelings about this story .. I'm in the first few chapters and why does everyone treat her like a baby making machine? even the ml.. I get that it's how their society worked but it's still pissing me off. . like even her maid thought it was crazy of her to want plan b... she's a barely 20 year old princess who was treated like shit all her life being taken as a hostage wife.... it'd be crazier if she wasn't scared of pregnancy... I'm not saying wanting pregnancy is wrong i just wish her concerns are given the attention and care it deserves