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But it won't work if all the kids die. Just the females.

Why?

If the males survive then they can pair with normal females and use up their resources. Say I have 2 boys, and 2 girls, all die that's 4 people who won't have babies. But say the boys live and marry 2 girls. Now we have 2 dead, and 4 who can't reproduce, for 6 total taken out of the healthy reproducing gene pool. Every male with the gene who finds a life partner also takes a otherwise healthy fertile female out of the gene pool as well.

https://en.wikipedia.org/wiki/The_Screwfly_Solution (spoilers for an sf story)

Even better would be a plot about a machine that would kill those kids in the bud instead to force the society to spend valuable resources on them for several years.

We could call it the condom's machine episode.

Like children of men but being done for the purpose of population control. That sounds like a good/scary sci-fi story!