Well, I'm not really sure that "poor should have less children" is inherently linked in conceptspace to "the rich / successful / intelligent should have more children". I'm not sure they're even very close to each other with a linking idea like "It is a good thing for the birth rate to be sufficiently large to maintain or increase the population of society"
giving free contraception to poor people could result in more children born to the most irresponsible subset of poor people.
We already penalize those poor who have excessive children in a variety of ways. For example, TANF doesn't provide for an automatic increase simply for having another child. Why wouldn't we wouldn't implement additional penalties to go with our new "Free Contraceptive Shots" program?
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.