If the end of government-issued/recognized marriage licenses spelled the "end of the traditional Amreican family", it would only be because traditional American families reacted to the change by choosing to dismantle their own families. Somehow I doubt that would happen, but maybe you know better than I do, since you're probably a member of one of those families, and thus are in a position to know that it would disintegrate if the government stopped recognizing your marriage.
And exactly what legal statutes are you referring to? The only ones I can think of are those that allow the government to exercise different controls on your money depending on whether or not it deems you "married".
The "traditional American family" is a myth.