How did Reconstruction governments benefit the South?
While this is, to some degree, a matter of personal opinion, I would say that Reconstruction governments did very little to help the South. For the most part, this is because the Southerners did not want the governments to do much that we would see as helpful.
One way that the Reconstruction governments clearly helped the South was by allowing them to return to the Union. The Reconstruction governments passed constitutions that were acceptable to the North. Because they did this, the North allowed the formerly Confederate states to rejoin the country without much in the way of punishment. This was certainly beneficial to the South.
There were other things that the Reconstruction governments tried to do that helped the South to some degree. These governments created social services like hospitals and orphanages. They put money into building railroad networks to help the Southern economy. Most importantly, they created a system of free public schools that were meant to educate both blacks and whites (including poor whites). All of these things were helpful to the South. The problem was that the Southern elites did not really want the government to provide these things. Once they got rid of the Reconstruction governments, they were able to dismantle much of what the governments had done. Therefore, the Reconstruction governments were not able to help the South as much as they might have hoped to help.