This might seem like a dumb question, I'm sure that every country has had some history of enslaving others/being enslaved. But too often I hear this phrase. I think the phrasing of "built on the backs of", implies that without slavery America would have failed; that all of America's success is attributed to the exploitation of slaves. Are there other countries with similar histories?
I have heard arguments against this stating that the North didn't have slavery and that slaves were actually bad economics.
If I have time tomorrow I will try to address some of your more specific questions for you (about whether slavery is bad economics in particular and the extent to which the US specifically can be said to have had its prosperity built on the backs of slaves, and whether this makes the US exceptional or not), but in the mean-time, you might find this old answer I wrote in response to the very closely related question "What role did slavery have in the industrial revolution, if any?" useful, where I talk about the experience of the US and the British Caribbean quite broadly in terms of slavery's contribution to western industrialisation. The summary of that answer is thus: I am not convinced by the argument that slavery was intrinsic to industrialisation in the sense that without slavery it would have simply been impossible, but it is likely that slavery was essential to the British imperial project in general (from which the existence of the United States stems), and very clear that slavery nonetheless had a huge and decisive role to play in laying the foundations for modern capitalist society in the United States.