You might be interested to learn that many defenders of the Southern Cause argue here that the South was actually very prosperous and wealthy -- on average far more wealthy than poor Northern farmers or factory workers.
How can that be? The answer is that slaves not only produced wealth, they WERE wealth, and so the South on average was quite wealthy.
Of course many Southern counties had few or no slaves. This was especially true in western Virginia, eastern Tennessee and western North Carolina. These areas remained hot-beds of Union sympathizers throughout the war.
And in Border States such as Maryland, Delaware, Kentucky and Missouri, where slave populations were barely 10% of the total, and slave owners correspondingly few, sympathy for the Southern Cause never grew strong enough to vote for secession.
But in the Deep South, where slave populations were 50% and more of the total, and slave ownership a matter of necessity and social status, then any perceived threat against slavery -- whether real or just imagined -- was both intolerable and a matter of life and death.
As to whether slavery would have died of its own accord in the decades after the Civil War -- that's very hard to say.
Yes, possibly in Border States and the Upper South, where slavery was never so strong.
But the Deep South is a very different story, and I don't see how they would ever have changed voluntarily.