I'm not from the South and we're not rich. I'm in my 40's and call my parents Mommy and Daddy. My dad and his siblings called their parents Mommy and Daddy. Don't care what anyone thinks about it.
I’m probably in the category you’re talking about- NYC trust fund kid? I’m not in touch with either parent anymore but I called my father “dad” or”Johnny” and didn’t call my mother anything.
My dad is from rural VA, and he and all my aunts and uncles (grew up poor) always called their parents "daddy" and "mama". One set of my cousins from this side of the family do the same (they grew up in their hometown). Me and my brother and another set of cousins who did not grow up in the hometown do not do this.
My co-worker (grew up poor), who is from a different town in rural VA, consistently calls her mother "mama." She didn't know her father. She's 58.
My SIL (grew up middle class), from NJ, calls her mother either mom or mommy. She's 55. So does SIL's cousin who is in her early 40's.