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?