That slavery was a dying institution is debatable. I've heard the arguments and they typically sound like pure revisionism to me. Slavery was considerable viable enough at the time that close to half the country was willing to wage war to preserve it, and the claim that it would have been economically unfeasible seems to confuse cause and effect by ignoring the fact that the southern slave-based agricultural economy was actually fairly lucrative up until the war. The southern economy was in shambles thereafter, but that's not all that unusual for the losing side of a war.
