But neither do married men have much better chances of such an outcome.

There is still a difference between "not much better" and "not better". I do not know the exact number, but if contact with your children is an important part of your utility function, then even increasing the chance by say 5% is worth doing, and could justify the costs of marriage.

(Even if the family law is strongly biased against males, it may still be rational for males to seek marriage.)