In discussing marriage, we sought a legitimate state interest in the regulation of sexual relationships in the face of Constitutional restrictions. This was found in the need to protect children, and further in inheritance law.
There proves in the present to be yet another state interest in heterosexual sexual relationships, an economic interest. The currently declining birth rate hurts the future economy. Zero population growth might make sense in a Malthusian (Tragedy of the Commons) world in which resources such as food supplies are fixed, but in the modern world increasing population means increasing productivity, more wealth and more wealth per capita, and thus a thriving affluent society.
Of perhaps more immediate concern, the Social Security system is just the most obvious of numerous programs which relies (not entirely unlike a giant Ponzi scheme) on more people joining at the bottom and paying money into it to support those at the top drawing money out of it. An aging population, with more people living longer, taxes these programs, including our newly-expanded government medical program. For these programs to work, there must be large numbers of new workers paying into them, and a falling birth rate leads to exactly the opposite result.
It thus seems that the state may well have reason to promote and even subsidize relationships that are likely to increase the population by producing children--exactly what it is complained it does for heterosexual marriages that homosexuals want to share. But if the reason for government subsidy of marriage is that it increases the population by producing children, then that reason does not extend to relationships which cannot, under any natural circumstances, produce children.
Admittedly, homosexual couples might wish to have children, and so might adopt them. This certainly does contribute to the nurture of children into productive members of society (although some studies, contrary to the politically correct position, conclude that heterosexual couples are statistically the best parents), but it does not produce additional members of society, and thus does not increase the population. If the government wishes to increase the birth rate, encouraging heterosexual relationships is presently the only effective means of doing so.
Although there are experimental ways in which homosexual couples can have children, whether implanting a zygote in a man or artificially inseminating a woman, these still at this point require the involvement of both sexes in supplying the genetic material. Some work has been done exploring the possibility of combining two eggs into a zygote, and so eliminating the male contribution, but this is not entirely effective. For one thing, sperm appear to do more in the early process than fertilization, being involved in the protection of the zygote. Further, this process would only produce female children (no Y chromosomes available), and any policy decision to support this approach to population expansion would have major social policy implications.
Thus even if it were otherwise determined that homosexual couples ought to be treated equally to heterosexual couples, there would still be good reason for the government to subsidize the relationships of heterosexuals that did not apply to homosexuals, as part of economic social policy of population growth.
We have thus found at least three reasons why government might legitimately regulate heterosexual relationships by issuing marriage licenses and providing other legal considerations despite the judicial ban on any government intervention in sexual and sex-based relationships, one of which is also a compelling reason why government policy should promote heterosexual relationships. With that judicial restriction, it seems that it should be unlawful to issue marriage licenses or otherwise regulate or subsidize sexual relationships except in those cases in which children are a likely product of the relationship.