One of the major social changes that was going on in the South during this time was an effort to modernize the region and bring it out of its somewhat backward antebellum state. The desire to do this, combined with the reluctance on the part of some in the South to embrace the changes, was reflected in the Reconstruction governments.
One of the main things these governments were trying to do was to improve the lives of all Southerners by making the economy more egalitarian and by providing more in the way of government services. This is why, for example, the Reconstruction governments created the first comprehensive public school systems. They wanted to educate all the people where most children (even among whites) in the prewar South had not gone to school.
At the same time, however, the governments reflected reluctance among some Southerners to change. Many of the so-called scalawags were in no way eager to embrace black rights. This meant that the governments were not completely behind social changes of this sort.
In short, then, the Reconstruction governments reflected the desire to modernize the South, along with the reluctance on the part of many to take the change too far.