Hi and welcome to GreekChat!
I'm not sure I understand exactly what you are asking. As far as I can tell you said you were wondering why must Non-NPHC Greek Letter Organization(s) (do) know the greek alphabet. Are you asking why must we (non-NPHC greeks) learn the greek alphabet?
The reasons we learn the greek alphabet are probably similar to why NPHC members learn it. It is considered an essential part of our identity as greeks, plus we are able to identify and name other houses.
In reference to your mention about NPHC members who "rattle them off the tip of the tongues", I'm afraid I don't understand what you mean but maybe someone else could address this for you?