Ok, I'll clarify:

Your claim is that "hook up culture" is causing all these kids to grow up single-parent households. This flies in the face of all kinds of studies that show that, starting with millenials, kids are waiting longer to have sex, and are having fewer partners than e.g. baby boomers. At the same time, young adults are waiting longer to get married than baby boomers, are getting married less often, and once married are getting divorced at a lower rate than their parents generation. They're also having fewer children.

And yet, the number of unwed mothers has steadily risen in the past 50 years, only plateauing in the last 10 or 15 (at or about the time "hookup culture" became a thing that people clutched their pearls over). Why is that? I hypothesized, in my post, that there's an "(1) evolution of how people of child-rearing age think about marriage, or that (2) the changing shape of the economy means that marriage-as-a-mainly-financial-arrangement is dying a long-overdue death. (3) It's definitely not that legalizing so-called no-fault divorces allows women (especially mothers) to escape abusive situations that are, for one reason or another, impossible to prosecute as such"

So let's break those down.
Point 1 is sort of indisputable. Young people are waiting longer to get married (but also getting divorced less). Clearly, people are being more careful in who they choose to settle down with, including who they have children with.

Point 2 I claim is driven by the fact that single women are no longer obliged to treat their job as a match-making opportunity. Women make enough in the job market, and have enough jobs available to them, to not enter into marriages strictly as financial partnerships, that carry the obligation of sex and child rearing.

Point 3 is subtler, but also the main reason why just discouraging divorce will, I believe, actually lead to worse outcomes for children. Thanks to the various advances in women's rights over the last 100 years, a woman can actually get a divorce from an abusive spouse, without requiring police cooperation. This is huge. We are on a downward trend for domestic abuse, and a lot of that is because an abused partner can actually leave (and why you saw a spike in domestic violence during the COVID lockdowns) without the police getting involved. So the options are "have a single parent", or "grow up in an abusive household". Given how frequently abusers are themselves victims of prior abuse, I'd argue that growing up in a single-parent household is, ultimately, the lesser of two evils.

Speaking of police and their ability to choose not to make an arrest for a given event, there's my point about over-policing low-income communities. A person from a high-income community can get busted over 1.01 ounces of weed, post bail, and be back to work the next morning, then plea it down or have the charges dismissed, provided the police even stop them to begin with or think that an arrest is worthwhile. Meanwhile, a person from a low-income community has no choice but to take the months or years of jail time, for the same charge. And since we say "put police where the crime is", the police are themselves more likely to stop a "suspicious" person, and arrest them, because the police think there's more crime there too, and "going easy on them will just encourage them". All of this adds up to parents ending up in jail when they should be raising their kids, on charges that other people aren't even held for.