While I agree more or less wholeheartedly with the first part of your post, I have to say that, from my point of view, the role of human morality in practical affairs is mostly bugger all. In my opinion, it's all about shifts in power. In the case of slavery in the US, for example, the increasing industrialization in the north shifted power and influence towards those states at the expense of the southern states. This change, associated with a traditional rivalry between the north and south, urged people in power to support the abolition of slavery.
Another example of such change would be the fight for women's rights all over the world. The suffragists and the feminists would never have gotten anywhere if it wasn't for the two World Wars.
In fact I'd say amorality has been the biggest driving force of human prosperity, at least since the reformation, and probably even before it. What seems to me interesting about this is that industrial and economic progress seems to invariably lead to moral progress, as well. So, in my view, morality isn't necessary to progress, but the inverse is true.
P.S.: 3rd world countries are mostly not industrialized. And working in sweatshops isn't slavery. It's pretty close to it, but not quite.