Could you point to those statistics please?

I'm a bit confused how marriage protects against single person parenting when about half of marriages end in divorce.

Do you doubt that ending a marriage tends to be more difficult than ending other romantic relationships?

For all I know the difficulty and bitterness of divorce could make it harder for separated couples to co-parent, leading to more single parenting in families that start as married.

I'm not sure about that, I'm open to persuasion. But I'm not persuade by people saying {it's obvious}.

Actually, I should retract my previous statement. I don't really know what I wrote that, maybe something I'm personally reactive to.

As far as I'm aware what the family relationship counsellors are saying these days (the ones I've spoken to anyway) is that it is conflict that harms children.

It matters less whether the parents are together. What's important is that children aren't exposed conflict.

Is it a fact that everything else being equal, a lack of a legal marriage document causes more single-parent families? How did someone prove that?

Because if it's just a correlation, then you're might just be measuring the obvious third-cause: that deadbeat parents are not willing to marry. And that wouldn't be affected by preventing their marriage, since they wouldn't marry anyway.