Your post is the elephant behind the mouse that few will acknowledge is there: what is "priest" and "priesthood".  Is there really an "ontological" "mark" that intrinsically "changes" a person into "priest".
Another side of that multifaceted coin is, in my opinion, the absolute (not infallible) need to preserve institutional core - not as stagnant, selective ideology - but as identifiable, organized, evolving, quest'ing, dynamic spiritual and religious body that builds upon itself. 
Others: the nature of norms, selection, formation, certification, oversight, etc. Catholicism is deathly afraid to "appearing" to be ugh, p-r-o-t-e-s-t-a-n-t.