What small effect = no effect? I'm pretty sure that on average their welfare state would have been burdened by those children. Cost wise it was probably a win even with the later paied reparations. Are you willing to take a small effect = no effect position in general for say welfare state policies?
Read advancedatheist's comment. It wasn't about benefits exceeding costs, or the fact that successful Sweden adopted a policy providing Bayesian evidence for the quality of the policy. It explicitly offered the hypothesis that Sweden turned out better than average because of the policy, i.e. that it was a but-for cause rather than a tiny irrelevant effect in that direction.
There is no straw-man here, the difference is important. Policies with small maximum benefits are not individually worth huge political efforts or fixed costs. Policies with large benefits can be.
I recently read an article by Steve Sailer that reminded me about something I have been puzzled by for a long time. Relevant paragraphs:
Poor people having fewer children means that the children have more resources available per capita making the children better off. Rich people having more children actually increases equality in society since it reduces the per capita resource advantage their children have. Rich people giving to their children is also one of the few cases where the redistribution of wealth doesn't reduce incentives for wealth creation. Rich people care about their children too.
Since programs aimed at reducing teen pregnancy rates do seem to have had some effect, we known something like this is possible without being horrible to the potential parents it targets.
Yet a policy of "poor people should have fewer children, rich people more" sounds heartless despite increasing general welfare both by making poor children better off and by reducing the privilege of rich children thus increasing equality which we seem to think is ceteris paribus a good thing.
Why is that?
Edit: To test the source of the reader's intuiton (assuming he shares it with me), I encourage the consideration of two interesting scenarios that may depart from reality.