"polygamists, first cousins, gay people, etc., etc. If it were unconsitutional to have standards as to who can be licensed, then anyone could be licensed."
It is unconstitutional to have standards as to who can be licensed. And members of the groups you mention are certainly entitled to apply for and receive marriage licences. And they do too.
The restriction is not on who gets licences but on who they are allowed to marry. The traditional family of a few decades ago was, for example, limited to one race. Thus in many countries one could not legally marry a member of another race. That has changed now, in spite of arguments for the "traditional family".
The same thing will eventually happen to same-sex marriages, unless those opposed to them can come up with a better argument than "it's traditional".