What if... We focused on families, rather than "marriage"?

Okay, I (sort of) understand the rationale that drives so many conservatives to harp on "one man, one woman" marriage as the "bedrock of civilization" (for often poor reasons) and to position themselves as so-brave champions of the pure in a "war on marriage." For the highly religious it really does seem to stem from a bedrock-level worldview, something like the Great Chain of Being where there's a truly universal law that places God, husband/man, wife/woman, children, and everything else in a vertical hierarchy (in that order). I think that's bizarre and rather repugnant, but at least it does explain why we see such otherwise insane statements about how gay marriage will lead to a hermaphroditic universe. When gender-essentialism enters the picture, homosexuality truly is a Blue Screen of Death.

But for the red-blooded conservative who wants to uphold strong family values but isn't that committed to the Great Chain of Being, here's a possible escape clause from this seemingly intractable problem.

It really all comes down to what the government "should" support, and the conflation of secular-marriage and religious-marriage. Conservatives often claim that marriage should be about procreation. Okay; let's grant them that. (No comment about why anyone would bother officiating a wedding of an infertile hetero couple, for example... but let's grant it.) Yet barring true homophobia, one might still empathize with people in loving but non-"traditional" relationships, so what to do? Well, why not issue family licenses rather than "marriage licenses," to avoid confusion*? Basically, this would include the usual privileges afforded to married couples, but "family" is a far broader concept for most people than "marriage" is, even with gay marriage growing in acceptance. The key here is that a family agrees to mutually support and nurture each other—especially when it comes to rearing children. In particular, the most important thing about a family license would be the privilege of adopting since research has shown that children do best when raised by two or more parents (independent of parental gender, so suck it, prudes).

Consider this quote from the Heritage Foundation, a conservative think-tank, about the importance of families:
The family, centered on marriage, is the basic unit of society. Healthy marriages and families are the foundation of thriving communities. When marriages break down, communities suffer and the role of government tends to expand. Sound public policy places marriage and the family at the center, respecting and guarding the role of this permanent institution.

There's a lot of solid research to grant them this point about families, regardless of marriage—at least as any one religion understands it. The important thing about marriage per se is the contractual aspect: the ceremony and religious significance isn't universal, but the contract is. It's useful to have some legal recourse in the event of a negligent or abusive relationship.

So in this probably-won't-happen family license world, society and government largely wouldn't care about who shacks up with whom, except that there would be some slight social pressure to start a family as a means of contractually guaranteeing mutual support, and also (mostly from the conservatives) contribute to the future of society by conceiving or adopting children. Yet whereas various religions may define "marriage" as a sacred ceremony binding a man and a woman in holy matrimony, a family could constitute more than two people: extended relatives, polyamorous people, and so on. All that's required is mutual support and responsible child-rearing, if any.

Obviously religious doctrine is the big sticking point, here, but this sort of pivot might free up a lot of stress in the conservative leaning mind.

*I think "family license" is more meaningful than "civil union." The latter is just a wishy-washy euphemism for "almost marriage, except you can't have that."