So I read Reichert's original article, and Cardinal Pell did do it justice; however the journal First Things is a journal to advance religious ideas, and Reichert is trying to advance a viewpoint rather than being making an actual well-developed economic analysis. For example Reichert asserts (does not provide evidence for) that contraception means that women face "fierce" competition for men once they enter the "marriage market," and "this means that the 'deals they cut' become worse for them and better for men."
Simple logic tells us that every man who wants to get married still has to find a women, so men and women have about the same power from that standpoint.
In reality social and legal changes over the last few decades not caused by contraception have led to much greater power for women in relationships and marriage; for example GOMEZ V. PEREZ, 409 U. S. 535 (1973) reversed ancient common law, the wisdom of many generations, that if a woman wanted a man to support her child, she had to get married; the Court did so on 14th Amendment "equal protection" grounds.
Courts have become much more "woman friendly" in other ways also. Today a married woman with children can have an affair, divorce her husband, kick him out of the house, and her cuckolded husband must make large child support payments to support her and her boyfriend, who is now living with his children. This is common
And the cheated-on husband, when he tries to re-enter the marriage "market" is going to do so in an impoverished condition.
GOMEZ V. PEREZ is just one element in the social/legal changes that have made marriage more risky for men. The rise in the age of marriage that Reichert attributes to "the pill" could be attributed to these heightened risks and costs to men, and on the other side to the ability of women to access the benefits, such as child support, plus money and goods from welfare programs, that once could only have been accessed by her in a marriage.
If the Catholic Church wanted to help restore marriage using economic incentives it would advocate the restoration of common law in terms of child support, and advocate the end of government welfare programs, and only support private charity for "the deserving poor," ie widows and orphans. But the liberation theology influenced Church is supporting programs that are opposite of what would be required to restore economic incentives to marriage.
The pill shifted the power to young women. They can get all the “benefits” of marriage, while controlling the risks.
Men who want to be cads and women who want to be predators win.