A better chance of what? What exactly is a broke American going to do in a very poor country with sky-high murder and unemployment rates? I can't imagine a good outcome from this, unless they're sent as a missionary or some sort of NGO worker with the backing of a well-heeled org.
Haiti is a bit extreme. That is one messed up hell hole. But the broader point is fair - the world is full of opportunities, most of them not "here". The flip side is that there are plenty of opportunities here, too, and if someone can't seem them here, there is little reason to believe they'll see them elsewhere.
with a nanny state the US and European poor will always stay. it is the industrious middle class with skills who might move as is happening already in the UK. the grass is always greener on the other side of the fence. read up on the downside to being a 200k miner in australia.