Not sure what you mean by UNC system. North Carolina State isn't called UNC-Raleigh but it is part of the UNC system. East Carolina is part of the system.
UNC-Greensboro was founded as a woman's school. By the time UNC-W and UNC-C came along, there were so many established programs that it was pretty hard for a newbie to get a toehold. UNNC also has significant competition from an NFL team, not to mention an NBA team and NASCAR.
The state of North Carolina has five D-1 programs. Georgia, which has almost the exact population as NC, has two. So it's not like there's a pressing need here.