Lots.

I don't have a catalog of southern universities that I can toss into this response, but I can offer Drew Faust's well-researched, highly illustrative example: James Henry Hammond.

James Henry Hammond was not born into the wealthy South Carolina gentry, but he clawed his way there through "hard work" (read: the acquisition of slaves to work for him, but there was considerable personal effort involved as well) and, in part, attendance at South Carolina College.

SCC was a pillar supporting the aristocratic dominance of state politics throughout the antebellum era. This was a time when South Carolina had no comprehensive public school system, and most didn't even get to go to secondary school. People who attended SCC were a select minority that almost entirely came from the state's upper class (Hammond was one of few exceptions, as his father had strong connections to the school that got him in).

South Carolina was perhaps the least democratic state of the antebellum era. State government and institutions were overwhelmingly dominated by the wealthy planter class, who colluded and organized things to stay that way. SCC was meant to play a direct role in unifying, training, and bolstering the states ruling classes politically and socially. We know this because the state legislature said as much when they arranged to help fund the school. One critic of the process complained in 1842 that many citizens believed that "those educated at South Carolina College as alone fit to fill all the offices and control the destinies of the state." Twelve of 21 state governors from 1824-1865 attended the college, 3 of 4 state chancellors, 5 of 6 state judges, and a majority of the US senators (Hammond was one).

SCC's role was, therefore, not just academic. It's curriculum was designed to socialize the state's up and coming elites. They learned mathematics and language through rote drill that must have been awful, but they were also taught subjects like moral philosophy according to conservative southern thought. Hammond learned, for instances, that humans were not born in states of equality but rather hierarchy. One of his more radical professors, Robert Henry, mixed politics and education to specifically teach his students proslavery arguments on political issues like the Missouri Compromise, and that society would destabilize in the south if its institutions were uprooted.

A lot of the education of SCC students took place outside the classroom entirely. These were not huge SEC schools but rather small, intimate classes of around 40 men who were in constant competition with each other. Similar to how boot camp creates unity among soldiers by giving them a common adversary (the drill instructors), students at these schools bonded over pranking or ridiculing the teachers however they could get away with it. They learned to seek out and retain whatever power they could, and to dominate their personal spheres as much as possible. Such behavior would help them dominate their dependents throughout life--their wives, children, slaves, and (if they held office) lower class citizens of their state. It also taught them, as a society, to resist any challenge to their dominance (say, from the North...).

As Faust describes, the students learned that "self-assertiveness was so valued that no challenge could be dismissed as trivial."

To summarize, institutions like SCC not only had (limited?) educational value but also served to replicate the social institutions of southern society and reinforce social and political power structures within the state.

Source: Faust, James Henry Hammond and the Old South

Follow up: Would you even send him to university, especially if he was intended to inherit your land?