Earlier quoted context omitted.
The state has a vested interest in procreation (i.e.: creation of new citizens & taxpayers as others die off), so takes an interest in "marriage" as a means for facilitating the most efficient & effective means of promoting procreation, doing so by giving special benefits in return for parents taking on special obligations. Expanding the beneficiaries of those benefits to those to whom there is absolutely no chance (…
Marriage has nothing to do with procreation. The government doesn't care if you plan to have kids when you get married, there's no tick box saying "You agree that this marriage license is only valid if you have kids.". Marriage is about a union, that's it.
For most of human history, and without having to get into more specific details, a man and woman living together for more than a short time usually resulted in children. The institution was enacted to encourage such couples to avoid getting into such a situation unless they agreed to stay together, ensuring the likely offspring would be raised by their own parents (generally the best possible conditions).
There's no point in formal social recognition of a union if there's no chance of reproductive consequences thereof. And by "no chance" I mean "the notion is utterly preposterous", not "they may choose not to" or "parts don't work"; if literally two bits of information (one quarter of a byte) is enough to make the decision, that's enough.