You could also ask why Iraq did not remain peaceful after the war and supported an insurgency and still has a large cadre of people who believe the same things they did before the war.
One answer may be that the reason Germany and Japan changed was because the entire population saw the devastation of war and the spirit of the population was totally broken, allowing them to be rebuilt and re-molded along different philosophical lines. The South, like Iraq, was defeated in battle but left substantially unchanged in the aftermath.
I remember this being a big worry in the Iraq war when the 4th mechanized infantry was stalled by Turkish refusal to allow the U.S. to cross over its borders. The worry then was that if the victory came quickly and with only one region of the country exposed to the might of the U.S. military, it would leave the rest of the country in a situation of having ‘lost’ without ever seeing a battle or U.S. military power. That would leave them unbowed and hostile.
All that said… The South was not Nazi Germany. One of the things that ended the Nazis was the Allied policy of forcing citizens to actually march through the extermination camps and see what was being done in their name. Many were horrified and deeply ashamed, and that made them ardent anti-Nazis.
Maybe that’s the real answer. The Japanese and German populations felt shamed by their role in the war. The Germans because of the excesses of the Nazis, the Japanese because they were forced to surrender and that was shameful in their culture. Therefore, both populations were receptive to change. The people in the South felt more like they were on the losing side, but not necessarily the wrong side.
Don’t forget that the civil war was about more than slavery, although slavery was a major factor. The south seceded for a number of reasons, including the general feeling that they were not being fairly represented and that the North was interfering in their lives too much in a number of ways. Lincoln won the Presidency without winning a single southern state and he wasn’t even on the ballot in 10 of the southern states. That caused a lot of anger. In addition, the Southern states were generally poorer, and the main economic system was built around plantations which they thought required slaves to be successful. To make matters worse, the north advocated trade tariffs that would negatively impact the south.
Therefore, the people in the South felt that social change in the north was threatening their economy (at a time when many of the people were subsistence farmers and barely surviving), and that the increase in population in the north from immigration was changing the electoral balance and leaving them with no representation. It didn’t help that the north was growing in wealth while the south largely stagnated.
After the war, many of these factors remained in place. The promise of reconstruction was not uniformly kept, leaving many southerners bitter. The emancipation of slaves didn’t have the dire economic consequences that were feared, but it did cause a lot of dislocation, further embittering the people. Bitter, prideful people are not easy to sway to your point of view.