But about 3 times as much new people are born, most of them in poverty....
In poor countries children are your retirement savings, so at an individual level having more children is a rational decision. In many cases they aren't having more kids than they can afford--they can't afford not to have more kids. Even at a national level it's not clear that lowering birth rates without additional changes would help a country economically.
So they are probably (well, not probably)... they ARE going to have more kids whether you like it or not.
The question becomes how do we (Western society, which has more resources than we know what to do with) address the issue and try to do good in the world.
Be involved in how your governments and MNC's behave in these countries. These entities are more likely to pay attention when you, as a voter or customer with more disposable income, say something compared to the citizens of poorer countries who have less of a voice.
It's a natural response to the hardship. If the chance that the kid make it is 10%, then make 10 times more kids. That way you have around 100% chance that your lineage makes it through life.
In other words: In a society where 90% of children die and women have 10 births, one third of the mothers will lose all. All assuming the deaths are independent of course.
I'm only 25 so I don't know how I'll feel in 10-20 years, but right now this is part of my consideration when thinking about long-term goals and whether I'd want to have kids at some point. I might, so for that eventuality, plan B is to adopt. Plan C is to have one (and only one) kid, which already turns two parents into one descendant, so that's better than nothing.
The only thing I'm worried about is that smart families will do this and the stupid ones produce six. It's in the education and not in the genes... but it's also in the upbringing, and if they're brought up with the mentality of the kind of people who currently get six kids...
We shouldn't turn to ideals in an effort to ignore or abdicate responsibility in dealing with the reality we are given.