"…the argument that we need to cut the pay of some women—those stay-at-home mothers who charge a fee to watch other people's children, for example—in order to help other women, and that this is somehow good for women generically, seems to me to be pretty weak."
The argument I made is an argument about gains from trade; Ponnuru finds it dubious. But since Ponnuru presumably prefers free trade in cases not involving free labor; since he presumably opposes protectionism when protectionism does not involve the market for jobs—let's just substitute a good for jobs. The American cotton industry has been similarly protected; let's start there:
The argument that we need to cut the pay of some cotton producers—American cotton producers, for example—in order to help other people who happen to wear clothes, and that this is somehow good for people generically, seems to me to be pretty weak.
It's somewhat disingenuous to refer to opening up a market as "cutting pay," but downward pressure on wages will be a result of allowing people to voluntarily contract for services. So fine then; we're cutting the pay of carmakers when we allow foreign cars to be bought and sold in the states, and cutting the pay of sugar producers when we dare import sugar.
You can also play this game with candle makers or shrimpers. Closed borders constitute labor protectionism. There's no way around it. As Jonah Goldberg argues, free trade in labor will involve problems of absorption and assimilation that free trade in goods will not. But anti-immigration free traders need to make a case based on the relevance of that difference, because the economic logic behind imported goods and imported labor is identical.