I am with @skieurope that the little Ivy, southern Ivy, etc. labels are ridiculous. Ivy League is eight schools. Whenever anyone says of my son’s college, “That’s a little Ivy, right?”, I say something like, “Well, there are only eight colleges in the Ivy League, and Williams is not one of them. But you’re right that it is a really great small liberal arts college. He is having a wonderful time there!”
A southern Ivy is… Princeton? The southernmost member of the conference?
But terminology aside, I think the OP is making a valid point is that there are some excellent colleges in the southern U.S.
(This reminds me of an episode from “My Crazy Ex-Girlfriend” when a character gets into Emory and keeps telling everyone, “It’s the Harvard of the South,” and people keep saying things like, “I thought that was Rice,” “I thought that was Duke,” “I thought that was Vanderbilt.” And then he meets someone who says he is from Harvard, and he asks, “Which Harvard- of the south, the midwest, the public Harvards?” And the person says, “No, it’s in Massachusetts.”)