As I thought was pretty clear, I'm not talking about single parent households at all, but rather the old fashioned social necessity that the parents bother to get married. Married or not, its a cohabitation situation with exactly the same parental responsibilities, and the relationship between the parents does not need to be civilly codified. Obviously, I pull heavily for healthy relationships, especially where kids are concerned. What I don't think is crucial is distinct from that, and basically boils down to both signatures of a piece of paper. The paper doesn't matter. The relationship does. Parenthood does. Neither of those things need have anything at all to do with the state.
My aunt and uncle for example have been together for longer than I've been alive, raised a family together, and never felt much of an urge to "make it official". What have they got to prove? There is no need for a legal document to exist in a relationship to legitimize it, nor a religious ceremony.
What matters is responsible parenthood and a meaningful and healthy relationship. As opposed to the ongoing shitstorm that is half the marriages I've seen, which then come crashing down, damaging all parties.
Anecdotally, from watching my friends and family go through their marriage-divorce cycles over the years, I've noticed that the people in committed relationships who never seem to get around to actually cashing in on that extra tax benefit (if applicable) seem to be somewhat better adjusted and have more stable and secure households. For whatever reason...probably some massive sociological factors that have been driven into everyone psyches by media and family, a lot of switches seem to get thrown in people's heads when they get married and they start getting weird. All that programming is maybe causing some bent expectations and resentments? Dunno.
For whatever reason...I've seen quite a few relationships wind up on the rocks as a consequence of bringing marriage and all the baggage that comes with it into the picture. It was a huge concern of mine before I got married, as we'd been together for quite some time, and it had been going extremely well. So far so good. Got married, came home...quickly realized that nothing in our relationship had fundamentally changed, and we were exactly as beholden to each other as before. No biggie. I like this thing, I'll keep doing it till I'm dead, or she bails.
I speculate that the hurt happens when people try to jump into socially constructed roles of "husband" and "wife", as opposed to the natural roles formed by the flow of their own individual relationships. People think and act differently, and this clashes with what the relationship started out as, ultimately having the effect of undermining it.
Honestly, if people spent even half the time on actually building and maintaing a healthy relationship, rather than "Let's get married because we are supposed to and that will fix everything", or "Oh shit we're pregnant, better get married. Cuz that will totally help", they'd be a lot better off. People go into marriage thinking its going to make things easier, or better, and it doesn't. Its different, somewhat, but end of the day, married or not, its a personal relationship with another human, as opposed to with another social/gender role.
Simply participating in a rite doesn't change that. Nor should it. Whats good for the kids is having two parents with a solid relationship and some stability. With divorces being the norm rather than the exception, I have serious doubts that marriage is intrinsically good for relationships or kids.