When marriage is decoupled from biology, there are at least two major consequences:
i) If marriage is no longer grounded in biology, if marriage no longer correlates with biology, then any "relationship" can be defined as a marriage, viz. homosexuality, consensual parental incest, bestiality, pederasty.
ii) Instead of gov't recognizing a natural institution–which is ontologically independent of the state–gov't constitutes marriage. Marriage becomes a purely political artifact. Gov't can confer or revoke marital protections at will. Gov't now defines ex nihilo the fundamental unit of society. This is just another plank in the totalitarian state.
iii) It might be objected that a biological criterion fails to rule out polygamy. Two points:
a) Even if biology is not a sufficient criterion, it remains a necessary criterion.
b) There's a difference between what is a marriage, and what is a good marriage. Polygamy is bad marital policy. That should be discouraged in various ways.