Actually, economic analysis in the 1850s by Frederick Law Olmsted and others indicated that paying people wages was more economical than slavery, due to increased productivity of wage workers. The thought at the time was that slavery would disappear in just a few decades.
Note also that slavery seemed to be on the way out in the late 1700s -- then Ely Whitney invented the cotton gin and created a huge industry around a new cash crop. The fact is that slavery was an anomaly. Fifty years after the cotton gin it was once again seen as a sloppy way to run an economy. It was limping along and would have withered away without the war.
Slavery would likely have died out by the early 1900's as a result of industrialization, but few probably foresaw that in the 1860's. The south in general sure didn't see it, and fought hard to keep it. The question is, would you have wanted to be a slave in the south during those few decades?