Leveling the Playing Field.

Why not... just limit the number of marital licenses granted annually in this country, similar to the way liquor licenses are regulated in plenty of communities?  Two-person, non-related "teams" of adult age would then compete for the more rare and highly desired civil license.

 (Religious denominations could continue to perform the sacrament of marriage under their own rules with no numerical restrictions on private licensing, and these unions would continue to be recognized by family, friends, and the larger community, but with no accompanying civil benefits or official recognition unless that right was won in the overall competition, open to all two-person non-related teams of adult age.)

If you win a civil license to marry but then later choose to void it, there's no getting back in line as part of another team to recompete...

If you come from a long line of happily married folks, you might get a slight credit -- legacy points -- to up your score, presuming you know how the game is played in its ups and downs.  But not so many points to disadvantage those who were not raised in stable, two-parent homes from competing honestly themselves....

Some of the challenges in the competition could involve child-rearing -- it's 3a.m., the non-talking  baby is sick and running a fever, will NOT settle down... what do the two of you, working realistically together, do?  (points deducted for wasting time verbally or physically expressing natural frustrations, and not working together in the best interests of the sick child...)

Toss in a few financial hardship questions  (not even the rich are immune in these too-big-to-fail days) and a few 'this is not how we planned it' tests when the ideals don't match up to the realities, and you might get a decent idea of who is gonna make ... we'll find out... in the long run ...

The winners of the coveted civil prizes could live with their spouses whereever they wanted -- secure in their rights -- and would have an obligation to live up to their highly coveted 'married' status.  As in the Hunger Games, former winners could mentor future competitors to help them up their games.

Physical and sexual competitions could also be part of the game, but not so much that simple studding means a marital license.  Afterall, plenty of people can rut and reproduce, but that doesn't mean their offspring is necessarily a net contributor to society, especially where the State has to step in -- pre birth -- to fund said offspring.

Some say, more is better.
More children = more future taxpayers. 
Hmmm... hypothetically, yes.
More marital licenses = more choices, more pursuits of happiness.
Ditto.

But what if we've got it all backwards, and less is more.
If civil marriage recognitions were limited, the product would be seen as more desired and valued accordingly, one would think...

With some good honest competition -- governed by set scoring rules; none of this popularity voting skewing legitimacy -- perhaps the institution would fall into favor again and we'd begin to grow a healthier society.  What we're doing now seems not to be breeding success...

Nevermind the Constitutionality of such a plan: 
if it works in reality, it's cool. 
Everyone will just be asked to play along patiently as we limit the licenses, and study the results.

There will also be an opportunity to change the competitions as society's needs/roles evolve, as well as the opportunity to vote thumbs up or down on whether the current crop of scoring judges continue on in that role.

'No confidence'* can mean an ouster or two, and nobody gets to rest on his or her laurels. 

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* “Same-sex couples have every other right,” Chief Justice Roberts said, sounding inane for a big brain. “It’s just about the label in this case.” He continued, “If you tell a child that somebody has to be their friend, I suppose you can force the child to say, ‘This is my friend,’ but it changes the definition of what it means to be a friend.”