beta
All I get from this is that the Japanese medical system sucks, and they don't care whether kids live or die. You're saying one of the most prominent hospitals in Japan doesn't have a pediatric department. Furthermore, you don't have any doctors well-versed in pediatric surgery and no residents willing to join the department. How does this make sense to them? Hopefully this is just a plot device used for the manga rather than an actual problem in Japan. Otherwise, that would be crazy.
Maybe I'm different, but I really don't like books where the omega/woman gets pregnant and doesn't tell the baby's father, especially if the baby daddy is a decent person. I find it kind of unfair, like that person misses all the milestones of their child and sometimes causes the relationship between the child and father to be strained when they meet later down in life. If the baby daddy showed signs of being abusive, I would not say anything, but it always seems selfish to me when the mother of the child chooses not to because of pride and fear of confessing their feelings. Like this only benefits/saves you, not the child. Especially because kids and people in general can be cruel, and the child may eventually feel some type of way from having a missing parent.
Anyway, this is just my opinion, I'm not particularly expecting people to agree.
Also, when I say abusive, I mean any form of abuse, whether physical or emotional. If the man is a narcissist or misogynist, it would also make sense that the mother may choose not to say anything. However, in cases like the first story, I truly can't see a good reason not to say anything.