There are so many problems with the OP I almost don't know where to start. What you appear to have done is abstracted the notion of gay marriage from a context of within the actual United States, and then given it the context of some bizarre, non-existent country in which all people contribute to society, marriages and only marriages produce children, benefits of legal marriage are distributed with the expectation that the married couple will have children, married couples contribute less in taxes, and that there is no extra benefit of marriage being legally recognized by the state compared to simply being married informally. All of these notions are demonstrably false. Let's take them one at a time:
1. All people contribute to their society: Do I even have to explain this one? Every one of you knows someone who is a leech on society. Expecting every baby generated to have a positive contribution to society and the "power" of the country is so wildly naive that I don't even know what to say, OP, I really don't.
2. Marriages and only marriages produce children: This is represented by a clear lack of understanding of word definitions in the OP: "A common byproduct is children, which is the real goal here." A byproduct is not a real goal. Marriage is not necessary to create children (I can't believe I'm explaining this...), nor do all marriages of heterosexuals produce children. Using your kind of argument, infertile people should not be allowed to legally marry either.
3. Benefits of legal marriage are distributed with the expectation that the married couple will have children: What the hell do hospital visitation rights have to do with procreation? Benefits of legal marriage are distributed to encourage marriage (how obvious is that?!). Marriage has been shown to be a stabilizing social factor. When people get married and stay married they often end up having a lower incidence of disease and death due to disease, among other advantages. Marriage is good for society regardless of whether or not marriages produce children.
4. Married couples contribute less in taxes: While there is a small tax-benefit of marriage, married couples often actually produce more in taxes than non-married people when you account for other variables such as propensity for crime, stability at work, general demeanor, incidents of disease, etc. The benefits of marriage creating stability for two people often result in them being better producers for their country.
5. There is no extra benefit of marriage being legally recognized by the state compared to simply being married informally: The social benefit of a group being legally accepted by its government didn't come to mind? If homosexuals are not allowed to marry while heterosexuals are, this creates a social air of heterosexuality as the norm and heterosexuality as deviant and abnormal. Legally endorsing a lifestyle bears obvious social fruits. You can see this with heterosexual marriage: being unmarried by a certain age comes with a negative stigma. Legalizing gay marriage will do a lot for the gay community socially. If nothing else, this makes it worth doing.
I think if you reexamine the OP with this in mind, you'll see how trite and superfluous it is. Nothing about it makes any sense.