Versailles fell into the trap Machiavelli warned against - to injure an enemy, but not so greatly that you do not need to fear harm from him in the future.
The Morgenthau plan was morally unacceptable as it was effectively a sanctioned genocide, and rightly rejected.
The failure is in several parts, though all of which fed into each other:
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The old elite of the Confederacy remained, and leveraged their social connections to restore their position of supremacy in the post-Reconstruction South.
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The South was allowed to cultivate a post-Reconstruction cultural mythos glorifying slavery and the slaver cause amongst the common people.
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The populations which were most resilient to the whole diseased regime, Black folk (on account of, well, knowing goddamn well they were the regime's scapegoat and underclass), were abandoned to the violence of white supremacist dominated state governments after Reconstruction.
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The economic system of the US South did not fundamentally change, in part because of #1, remaining an aggressively agrarian society based on the leveraging of the grotesquely undervalued labor of tenant farmers for plantation owners, by the lack of alternatives available for said labor.
The solution is simple, but requires great political will.
Hang or expel the elite. Seize their property. Redistribute it. Eliminate ideologues from participation in public life. Reconstruct (ha) the economy according to the standards of the North and Midwest.
In pre-information age societies, the elite are the primary perpetuators of such cultural mythos. With their absence, the 'Lost Cause' is greatly weakened - not to mention they don't get to spend a century shitting up academia. With the seizure of their property, their kin lack recourse to regain the status of elites. By redistribution of the land, friendly demographics are given firmer economic grounding and influence in their communities. By eliminating prior ideologues of the old regime from participation in public life, a major transmission vector for thinly-cloaked revanchism is extinguished. By the reconstruction of the economy, the essential material conditions which enabled the pseudo-aristocracy is eliminated.