The institution of marriage encourages biological parents to produce and raise children together which in turn benefits society as a whole. As marriage has become liberalized we have seen a decline in marriage and a rise in illegitimacy and infertility due to a steady increase in the ages of first time mothers. This is bad for society since encouraging reproduction is how the dominant religions and culture of today became the dominant religions and cultures of today. Populations change, and those that fail to promote high birth rates will be overtaken by those that do. Look at Japan for a good example.

There is a very basic fertility test that is used: making sure the marriage consists of one male and one female. A more complicated/expensive test could be added, but such inclusiveness and invasiveness is not necessary for there to be a valid reason for denying same-sex marriage. The existence of infertile couples doesn't discount the usefulness of this quick and dirty restriction or prove that marriage isn't based on procreation. This is because infertile heterosexual couples are the exception to the rule, infertile homosexual couples are the rule. Besides, as technology advances it's much more likely to fix infertility among heterosexual couples. We are no where near the point of being able to make a m/m couple fertile within their relationship.

Denying a marriage is not intended as a punishment. We don't issue driver's licenses to the blind, but it's not as a punishment, it's just a recognition that they're facially incapable of performing the primary role related to the license.

We can carry the incest consistently to say that siblings can't marry regardless of their gender.

Having no offspring at all is, historically, more taboo than having offspring with a slight risk of genetic defect. You might value no children more than children with a slight risk of deformity but that would be you applying your personal value judgments, and if you're willing to do that, you're in no position to say someone else can't apply their value judgments to say that a relationship which is incapable of producing offspring is worse than a relationship with slight genetic risks.