I guess I could see that, sorta, but to me Lakers Celtics takes the cake, I agree Yankees - Sox is huge as well, hard to choose, Lakers/Celtics I am much more familar with as I watched them all in my youth.
To me those 2 are 100% identifiable as Iconic, in NFL, UHHHH, the best I can come up within NFC is Skins/Dallas for a LONGGG time hated rivials(at least it was the 19 years I lived in the DC Metro), AFC I guess would be Baltimore and Pittsburg.
As far as Hockey, I been to a few prefessional games, but just never got into it, respectively.