If the Yukari system and the penalties for not following it exist only in Japan, why don't the Star-Crossed Lovers just emigrate?
That's a whole other can of worms to open. For one, the relationship might not work out for any number of reasons after emigrating, making the elopement pointless. For another, seeking refuge in another country requires a lot of sudden changes that some folk just aren't ready for, especially teenagers like Yukari and Misaki.
There's no explanation about how the system is supposed to handle gay people like Nisaka.
They probably don't care, as long as a child is produced from the marriage. There have been cases where a homosexual partner in a heterosexual relationship has a kid with their spouse. If not that, then they could pretend to be childless for a while while they sort everything out. And given one of the extra chapters, it looks like they pressure the couples into having sex anyway, as we see with Yukari and Lilina.
Later manga revelations show that the government sends them notices to be matched off with other LGBT if they know the kid is one themselves. They at least allow the individual to leave their pairing up to choice; either to clinically come out by revealing this status on official records, or hide it via paper marriage with each same-sex partner getting legally married to an opposite-sex partner of another gay partnership. They straight up admit that they won't be able to legally marry though.
Piggybacking off of the above, if the point of the system is to bring up reproduction levels, what happens with people who physically can't have children, like impotent men or infertile women? Would the system just pair them together to keep out of the gene pool, or would they give them a free pass?
Or intersex or "developmental disorders" like AIS, among others.
Chapter 261 gives off the impression that they straight up won't get notices at all, such as Nejima, who was predicted to die young.
Fridge Horror
There's nothing stopping government officials from lying about certain matches or forging papers. The only people who know the exact schematics of how Yukari marriages work are in the government, and hardly anyone questions it anymore or just eventually goes along with it. What's stopping some officials from pairing their children up with anyone they want, from any walk of life?
For the same reason that police officers can be charged for using government systems to stalk someone, find out their personal information, etc. There will be login records, as well as which records were accessed, changelogs, etc. All of which would require you to rope in the system administrator to alter, even assuming he can. On top of which, only the people in charge of developing the compatibility algorithm that matches prospective couples would be able to know which parameters to tweak in order to achieve the "perfect match" between any two prospects.
The story reveals that at least a good number of people stay in loveless marriages just out of convenience just to avoid the discrimination that comes from being divorced. Loveless couples may only have one child just to avoid scrutiny, but, depending on how that shakes out demographically, Japan may still not even be above replacement level when it comes to their population. But that also still means there are potentially a lot of unhappy people stuck in damaging loveless relationships for appearances. Aside from adding one big question mark to the actual success of the Yukari System, since there is no way to know how many couples are truly happy and how many are not, this also raises other questions; how many people stay in abusive households just to avoid the stigma that comes with divorce? Japan is already well known for its terrible handling of domestic abuse issues now; the Yukari system would only exacerbate the issue. Also, how many couples decide to move abroad from Japan, just so that they can get divorced in a country where the Yukari system doesn't exist, and never come back? How many people cheat on their spouses, visit brothels, go to sex clubs, or engage in swingers parties, just to get around these issues? How many kids are brought up in homes where there is no warmth because the parents barely talk with each other, and what effect does this have on future generations? The story infuriatingly refuses to answer any of these questions or considerations, despite being obvious issues that arise out of a system like this.
