I think his material point was that dealing with custody matters for never married parents is no more, or less, messy than dealing with custody for married parents. So what's the benefit drawn from being married?
I can tell you right now, if you go into a family court here in the US believing you will get more access to your children because you were married, you're liable to be disagreeably surprised. Whether married or unmarried, just protect your legal rights as best you can. And, no matter what happens, abide by the judgement of the court. Appeal later if you're upset.
There are significant custody-related benefits that accrue only during marriage, like for example being allowed to pick your children up from school, medical decisions, etc., that automatically flow to married fathers that don't flow to the unmarried fathers who don't have the proper paperwork on hand. (As with all things related to domestic laws, this is highly jurisdictional.)
I can tell you right now, if you go into a family court here in the US believing you will get more access to your children because you were married, you're liable to be disagreeably surprised. Whether married or unmarried, just protect your legal rights as best you can. And, no matter what happens, abide by the judgement of the court. Appeal later if you're upset.