I think you raise some great points. I would add to your list, that "palimony" brought to the table a completely different set of problems. A person perhaps deliberately didn't enter into a marriage agreement because they didn't want the baggage, or the benefits that come with it. But, then some years later the relationship ends and they get stuck with a district court judgment that says their girl/boyfriend is entitled to half their property and a monthly stipend. Not very fair, IHMO.
On the other hand, there are social benefits to marriage that cannot be denied. Children do better when there's a nuclear family present. Perhaps the people, as manifest through government policy and laws are correct to encourage the continuation of the traditional marriage contract. It's a complicated issue and one that I frequently find myself torn.
But there is no inherent connection between government-recognized marriage, and a "nuclear family" being present for children. Many children have parents who are government-married, even though their father (and occasionally mother) doesn't live them, and in some cases the children haven't seen the nonresident parent in years. In poor families, this sort of situation is likely to go on indefinitely once it gets started, simply because the mother never has a few hundred dollars to spare on something as non-urgent as undoing the formality of government-marriage (which soemtimes results in a rude shock to the children years down the road, when they're adults, and their mother dies, and her small estate automatically goes to her government-husband, tax-free). And of course, starting out with government-married parents doesn't mean the parents will stay government-married (or any other kind of married).
In Sweden more than half of children are born to unmarried cohabiting parents, and in a large percentage of these families, the arrangement is permanent; some get government-married a few years down the road, but many don't bother.
Where you see strong statistical correlations between government-married status of parents and children growing up in a two-parent home, it's just that -- correlation, not causation; it's just a cultural phenomemon that people who predisposed to form and maintain stable families get government-married. But very few of those would manage their marriage differently if it wasn't government recognized/licensed. A large percentage of stable families with government-married parents hold religious beliefs that teach that marriage should be permanent, and the decisions they make regarding their marriage are driven by their religious convictions, and not by the government recognition program. If the government stopped recognizing marriages, these couples would still get married in their churches, synagogues, or mosques, and would still consider themselves married and be considered by their social community to be married. And non-religious people who simply believe that permanent marriage is the ideal foundation for society would also continue to get married in privately officiated ceremonies, and stay married at the same rate as if the marriage had been government-recognized (excepting the previously noted phenomenon in which low-income people are more likely to stay government-married even long after the actual marriage has ended, due to lack of funds for legal costs).
Frankly, I think religious groups should be taking the lead in ending government recognition/regulation/licensing of marriage. When you hear a member of the clergy saying "By the power vested in me by the state of ____, I pronounce you man and wife", that should be a loud red flag that there's a problem here. No religious official should need permission from the government to perform a religious ceremony, and they would do well to drive home the point by refusing to report marriages they have performed, refusing to sign any government documents concerning marriages they have performed, and refusing to inquire of couples requesting marriage whether those couples have acquired the government-mandated license. It wasn't all that long ago that many US states had miscegenation laws on the books, preventing mixed-race couples from obtaining marriage licenses, and thus making it illegal for a member of the clergy to marry them, even if the beliefs of the religious denomination endorsed mixed-race marriages.