No. No way.
I was thinking in terms of the informal arrangements families have always made, taking in orphans or nephews or grandchildren and raising them, taking in family members or friends who had no place to go, but who then become essentially members of the family.
At one time people understood and respected these kinds of informal family arrangements but in the modern era you run into legal issues involving schools, medical care, and the like. I've been through it several times over the years and have had to finesse it various ways.
The kind of "legal space" to define your own household may or may not be practical in the modern era but the need for it is there, anyone who has informally "adopted" people into their families for whatever reason has run into the kinds of problems I'm thinking about. This kind of thing was becoming less common for a few decades but is returning, you are seeing it again more and more.
Thats what I was referring to. But as for marriage, no. Government has no right or authority to try to re-define marriage for all the reasons you refer to and for more basic moral reasons too. On that I'm with you.
I seem to remember that sometime in the past few years, the City of San Francisco had an ordinance that all employers had to include gay partners in employees' insurance. The Abp of San Francisco tried to work it out that Archdiocesan employees could designate one person as co-beneficiary on their plan, no questions asked about who that person might be: wife, husband, son, daughter, gay partner, business associate, or random-person-on-the-street.
If I'm remembering correctly, the City's response was: no, not good enough, nyet, ningun, nada.
But admittedly, San Fran is particularly narrow and bigoted that way.