People in South and North Carolina do not see each other’s school as rivals. Yea they may say “Real Carolina” but they are in no way big time rival.
NC vs NC.St yes But not SC vs. NC. In fact you’ll see NC fans at SC games and vice versa.
I don’t think the NFL wants three city teams in California. I get the feeling for some reason they want it to be like NY. Two teams in the largest cities, one team elsewhere. LA and San Fran, NY and Buffalo.