First, because an organic and social solution is far more humane than asking each couple and infant to be verified by a test procedure. It insults the integrity of families to suggest they should ever have to undergo genetic testing in order to attain legitimacy, rather than simply following in the steps of publicly declaring a marriage commitment beforehand. If the two are married, no proof or suspicion of any kind need be offered; this is immediately the man legally vested as father with zero additional proof or documentation -- and testing is only for the broken cases where a challenge and accusation is at stake, but these are inherently ugly to deal with.
Second, because marriage isn't just a paternity test, it's a preparatory gesture that is rightly given great favor and advantage in the law (not nearly enough today, to be honest) as incentive. In every single cultural and historical corner of our planet, it has marked a social event that not only unifies two people, but involves their families and communities in explicitly recognizing and making a place for a new family branch; community witness to marriage always meant more than simply notarizing a form, after all. To ensure as much as possible that birth happens under the conditions of advance commitment, recognition by extended family, and declaration before some community of persons is one of the most important goals of making any family law or legal structures humane and functional.
