I feel like a good explanation on what exactly the Devouring is in the context of the canon and this story is in order, as Shirou is not aware enough to have figured it out, unlike if Rin had been in the picture. As even if you go to the source material, there are a lot of hints about what it is, but it is hard to piece together until the very end.

The Devouring is an illness from the body taking on too much mana, because, just like in Fate canon, mana is poisonous, and it is far more poisonous here than in Shirou's world, because even when refined into Od, it can still kill you.

Even adults who have mastered controlling mana will still die if they don't regularly release it.

This is why you have things like Feybeasts running around when supposably there isn't enough mana for the plants to grow. It isn't that there isn't enough mana, it is that unrefined mana is toxic and kills the plants.

So what does the Devouring actually do?

It doesn't just slowly kill you, it damages the individuals soul, stripping them of everything. As it progresses, the individual becomes a blank slate who displays having all of the elements because the elements are present in the air, and their own mana signature is no different than that of the air around them. (This happens to everyone with untreated magical abilities, but it is supposed to happen faster to commoners for some reason)

In its latest stages, a victim of the Devouring is no different than how Shirou was after having his soul burned clean in the fire. And once in this state, they can be imprinted on, changing there element, origin, memories and even the nature of their soul into that of whomever imprinted on them. In canon, the change can go so far as physically transforming the person into whomever marked them with there mana.

Basically, they attempt to reconstruct there own souls with whatever material they are given in order to survive.

This is how Myne ended up inheriting someone else's memories. Though the Japanese girl didn't have any magic of her own, so she didn't physically transform into the person who marked her. (It is stated by Effa, in the LN, that Myne had been having vivid dreams long before then)

Myne ended up marked by Shirou because he used his Od on her body, but he didn't do it to the extent as to have an effect on her personality or physiology, despite low-key making her a familiar on accident. And if she is going through the Dream Cycle, she is so used to that as to not even think about it, as even before inheriting memories for a girl from another world, Myne had been seeing visions in her dreams whenever she had bad episodes.

So in canon, when the bad guys were trying to gather Devouring children, it was to make an army of these pseudo clones. And by forcing the people to give their names as part of marking them, the person who changes them has total control over them.

Naturally, a more powerful Devouring Child results in a more powerful puppet clone, making Shirou's kids highly desirable to those who know what the Devouring is. Valuable enough to try to kidnap them.

There is also a misunderstanding about what is outside of their not so little country, as it isn't a giant wasteland.

Early on in the story, it is revealed that sugar is a resent import from outside of the country. Not something that could be grown in a wasteland.

The extremely toxic mana is likely only a problem inside of their boarders, but they all stay there because it is a place where magic and the blessings of the Gods can be gained. So as long as you have enough mana to keep the country stable, it is a damn good place to live with a lot of benefits. It's only when mana runs dry that it turns into a death trap.

Another interesting thing to note is that the need to balance mana between parents might not be a thing outside of the walls. Why this would be, I don't know.

It isn't ever said to my knowledge, but there are reasons to think that this is the case. Though we will likely need to wait till the story finishes translating to find out.