And there's the crux of the REAL problem: the use of state-sanctioned marriage to carry a politicized load of obligations and "benefits" under force of law.
Current tax and employee-benefit laws push, first, the provision of insurance and other benefits through employers; and second, the "convenience" -- even with duplication among two working adults -- of having these linked to spouses. The "marriage penalty" in the income tax for two working spouses is only a feeble counter-cost to the much broader benefit of employer-provided health insurance.
The linkage of marriage to governmental benefits and favors in the welfare state has the same dynamic. Smaller single-parent counter-costs (AFDC, WIC) are dwarfed in economic impact by marital benefits (Social Security, most of all).
It's the removal of such required linkages, between marriage and private-but-nearly-forced or governmental benefits, that would remove the real problem. Along with state sanction or invasive force to support other marital "benefits," such as the enforced and sole right to hospital visitation. (One such linkage is, fortunately, being largely removed with the abolition of the inheritance tax.)
When marriage -- obligations and benefits -- is removed from the purview of the State, the usual dynamic of a free society will re-emerge: Those valuing a marital commitment will carry it out, and find religious and other supporters to carry it out, on their own voluntary terms. Not with ulterior motives of gaining government-mandated bennies.
Government is a lousy moral teacher, but that's the role this neocon writer is demanding. If a "Marriage Amendment" were passed, it would be as successful at stopping the seeking of marital alternatives as the Prohibition Amendment was at stopping the market for alcohol. Namely, not at all, except in adding costs -- such as hiding one's activities from the police, making alternative institutions outside the State's purview, and weakening support for the rule of law.