If that is the governmental purpose then a fertility test would be in order so those who are sterile don't defeat the governmental purpose and slip into the inner sanctum of legal status.Let's distinguish definition and purpose. Right now the definition is very clear, and the governmental purpose is very clear. Your proposed sterility testing muddies the definition. It also has no basis in tradition.
regarding the fertility test. It is sarcastically posited to show that reprduction is not the purpose of governmental sponsored marriage. The lack of a test and requirement to reproduce indicates a lack of seriousness about that goal. In fact many people seem to be reporducing without the benefit of governmental sanction.
This example is meant to counter the argument that marriage is for procreation and therefore homosexuals cannot get married. But infertile heterosexuals can do so.