As a guy, I find this pretty disgusting, and stupid.
The selected women are a "national treasure", yet only the selected men get to choose who to couple with? No option for the woman to reject? Yeah, that's rape, and a fundamental violation of human rights.
"Best genes"? Objectively, there's no such thing. You would need criteria. Desirable genes would need to be shared between the two to ensure the greatest probability of the genes expressing as dominate, while you do not want the people to share undesirable genes as those can go from recessive to dominate. If any selected male can choose any selected female, there's no telling what you'd get. You would need pairing controls, so the women in a group have undesirable genes different from all men in the group. Even then, it gets complicated, because genes often have multiple roles, so while it may do something beneficial in one system, it could be detrimental in another. Meanwhile, yet another gene might mitigate the detrimental aspect in some way. Like a Jenga tower, if you start moving around blocks without understanding how they support one another, the whole tower will fall.
Honestly, if they have enough understanding on what each gene does to legitimately make a valuation on the "best genes", they could just splice the code themselves in a lab, fertilize the egg in a lab, and implant it into any suitable surrogate. One donor male, one donor female, and thousands of surrogates. You could generate far more "super children" this way than some half-assed eugenics rape.
For something supposedly sponsored by the government, the "vending machine" hamster ball just pushes this into absurdity. It's stupid.
Thank you.
This gives me mixed feelings. I can see it being interesting if that guy on the train went all Rambo and decided to rescue her. But vending machine girls? As a woman, I find this a bit degrading.