https://www.educationnext.org/international-look-single-pare...
In any case, nobody ever linked ‘adultery laws’ with school.
There are many ways to incentivize nuclear families and discourage illegitimacy.
And, many ways to do the opposite.
In US, for whatever bizarre reason, society had been trained to recoil at the idea of a nuclear family. Indeed, some readers will reflexively gag at my use of the term ‘illegitimate.’
It’s strange.
Occasionally you get these stories where people are ‘shocked’ that a kid in Baltimore didn’t go to school! Yet, the fact that he has no father is just ho-hum. Missing the forest for the trees.
* The law treated illegitimate children as illegitimate. It was harsh to be born out of wedlock. (https://www.hg.org/legal-articles/inheritance-rights-for-leg...). No child support. No inheritance. Etc.
* Until recently, there was no no-fault divorce. You couldn't up-and-leave a marriage without good cause. If your husband was beating you or your wife committed adultery, that was a valid reason. If you got bored, existential ennui, or married for child support in the first place, you were SOL unless the other party agreed. People were expected to make it work.
* All sorts of fraud laws around sex and sexual behavior. If we had sex because I promised to marry you, I was expected to marry you. Marriage was viewed as a legal agreement.
... and so on.
Most of it had problems, but there were some good ideas in there too. Adapting those to a 21st century framework of equal rights would be challenge, both intellectually and politically. There was a history of perverse, unintended consequences, intertwined changes, etc. and a discussion like this would be a political hot potato.
Divorce is also a massive industry and political lobby. It intertwines itself with social justice and feminism, so it's hard to tease out, but a lot of work is actively done to break up families, since lawyers, guardians ad litem, etc. profit. A lot of that hits low-income families, despite low-income divorce happening without bringing this industry in.
In my line of work, I know of men who have upwards of a dozen children from just as many women. There is nothing in the law that deters this activity. Nothing. There used to be. And, when there was, it didn't happen.
Penises and Vaginas, orgasms and lust, haven't changed one iota in the past 10,000 years. I have little patience for those who wring their hands, fretting about how to stop this insanity. We know exactly how to stop it. You can open any legal code older than 100 years and see exactly how it is stopped.
The fact is, this society has made the deliberate and intentional decision to eradicate any responsibility on the part of men, leaving women absolutely fucked (and the daughters of these women even more screwed.) Ironcially, it was all done in the name of feminism.