This is another part of the problem. We are not "rewriting laws defining marriage". We are rewriting laws restricting who can enter into marriage. There is a difference. Who can enter into marriage does not define what marriage is. How marriage works defines what marriage is. Marriage as a legal contract is remaining completely the same in how it operates.
Marriage is still about stable, intimate, adult relationships in which the laws are granting certain rights of kinship and more specifically giving closest next of kin status to an intimate partner, since this takes away the need for a lot of paperwork to do the same thing. Many of the benefits of marriage comes from the fact that the vast majority of intimate partners build their lives together by deciding what each person will do to contribute to helping each other and go through life together. The vast majority of those getting married, particularly legally married, do so with the intention to stay together til one of them dies.
Intimate relationships between close family relations are not desirable and for the most part not legal. We have plenty of data to back up a true concern for genetic and/or behavior issues in children that result from these relations. In addition, many of such relationships start, at least to be encouraged, prior to age of consent. This brings up a question of undue influence in these relationships that does not exist for the vast majority of normal couples who get married.
Polygamy has nothing to do with the relationship but rather to do with the way legal marriage operates as a contract. Medical decision making for a spouse is granted with marriage. Outside of marriage, this is granted with a medical power of attorney. A person is only allowed to designate one person as their medical decision maker outside of marriage. There is also the issue that many people do, even without it being legal, abuse plural marriage as a way to oppress women and/or ostracize young men because it becomes one man with many wives which creates a shortage of women for other men and treats women as less than their husband. Many marriage laws would have to be changed to accommodate multiple spouses for very little benefit to society itself, not when we do consider the sexes in marriage equal. Any plural marriages would have to be agreements between all spouses, not just one person having multiple spouses in order to ensure that everyone is aware of the situation, since a major part of marriage now is protection in case of a breakup of the marriage. I'm not even against allowing a form of legal marriage that applies to people wanting multiple spouses in one big marriage. I just know that such a thing will not work with the way marriage operates right now. And the issue does not have to do with same sex couples being allowed to marry, anymore than it had to do with interracial couples being allowed to marry.