Only for the legal protections that marriage offers, such as where there isn't a will, so otherwise money/assets would be paid out according to intestacy rules, in which unmarried partners have no rights. Likewise in the case of serious medical issues where the unmarried partner has no legal right to a say in the treatment etc, and the legal representative can be a parent or sibling. And, again, as to who has the legal rights to care for your child - yes, your partner would have rights as parent as long as child were theirs, but in "blended" families or where the other parent wasn't known, you could be back to the parent/sibling being legally responsible. Also with life insurance, pensions, "widow's" pensions, etc., the absence of a will/deed of wishes, and the absence of a marriage certificate, could mean the monies go to the deceased partners' parent or sibling or child, rather than to you and your own child.
For me, marriage was all about protection, which is why I would never have bought our house jointly with my OH and certainly not had a child with him, without that marriage certificate.
Obviously, different if I was going to go it alone without a long term partner, as then it's obvious there's no one to marry, let alone get married, and if that had happened, I'd have been very careful with my will, deeds of wishes, beneficiary choices on pensions/life insurance, etc., to be crystal clear as to who would be looking after my child, the uses of the money I'd leave, and also a clear declaration in medical records as to my medical wishes and who was to make important decisions (NB it wouldn't be my legal next of kin, that's for sure!).