As coach commented there is the tuition factor, but also there is a de facto boundary of religion. 95% of the kids are Catholic and if they are not they pay higher tuition.
I have been a student, player, coach, and parent at Catholic. My senior year at Catholic was during the first attempt to oust us in 1986. Then as now it was sour grapes by those that don't want to work to get better, but make excuses of unfair advantages. I can remember all the accusations then that are similar... Their kids are smarter ( So Yale should win the National Championship every year ), They don't have to take who ever comes out... That goes both ways we don't get a lot of physicality, They can recruit... my favorite, have you bothered to look at us, We all went to school together from kindergarten guess they were recruiting us back then.
Does Catholic have an advantage? In some ways yes... Shared religion ( face it you have to just accept the fact that Catholic's are better at playing football ) very homogeneous make up of students, which allows for a consistency of scheme and philosophy. But they certainly don't have some advantages that other schools have. That same homogeneous make up creates a lack of diversity of student population. Tuition eliminates many from attending. There is a percentage every year of students who aren't able to move up from the middle school due to cost. I have also seen other privates offer our kids from middle school lower tuition at their school to come play for them.
When all is said though, over the years there are not many schools in the NCHSAA that have been better members of the association and gone above board to play by the rules than Catholic.