They clung to the existing system as much as they could, but the extra steps they had to go through (keeping people as slaves even when it was illegal but hiding it from the relevant officials, the overhead of using prison labor, etc.) wouldn't have made it economically viable even if they didn't have to rebuild a completely destroyed infrastructure on top of that.

But it took a long time though for the stored wealth (and associated power structures) to disappear. Around 50 to 75 years. It wasn't until the New Deal investments of the late 1930s (in the entire country, including the south) that the south stared to recover. Before that there were a lot of parallels to Iraq and Afghanistan. A destroyed country with US contractors taking an obscene amount of reconstruction money and not really doing much with it. Locals clinging to their existing way of life including secretly joining brutal militias to enforce the former power structures; some trying to bring "law and order" back to their locality in a distinct power vacuum, some trying to bring back power structures that they had internalized as moralistically correct. That's how the KKK started, with a lot of parallels to ISIS.