I understand what you're saying and what I say now might sound insensitive but this is how I see it: Humans try to bunch the endangered species together so they can breed and increase their population. They aren't allowed to be taken in as pets because these species are close to extinction, regardless of how much the family might love the animal. I think the case here is similar to that. Humans are endangered species and higher beings like Miria and Salem are trying to protect them lest other species get hold of humans to sell them in black market, sort of what Rider saved Mori from earlier in the series. So it is good that the system is apprehensive about letting humans out with anyone. Even Miria had be very harshly judged before they were granted custody. This likely to happen to Delver too and they still might not let Lily leave with him, precisely because she's ill.
It's sad but that's the whole point of this story.
Unsolicited opinion BUT this is lowkey making me mad. I mean, we have this dude who wants to care for a child who has been abandoned when she was a baby (intentional or not). His intentions are obviously good and he wants to ensure the kid is safe and happy. That's a fucking good parent material. If the higher being or whatever really wants what's best for these kids, then they SHOULD be doing whatever they can so these kids get to go home to THEIR OWN parents (biological or otherwise). Instead of using that so called almighty power to stop the reunion that'll obviously be the best for the child, WHY NOT MAKE AN EFFORT TO ENSURE SHE HAS HER OWN FAMILY INSTEAD??? UGGGHHHHH