So is Psychic really crap typing?
Should I use Psychic on Gorebyss (Toxicroak!)? Also, should I bother with Psycho Cut on Gallade and Medicham?
Psychic isn't "crap" typing for the sheer reason that it resists Fighting. Fighting is such a common attacking type, having a Pokemon that resists it without picking up a nasty weakness to Rock (Bug, Flying) or Ground (Poison) can make all the difference. Of course, Ghost has a better resistance to fighting (immunity), two shared weaknesses with Psychic (Dark and Ghost), a resistance to Psychic's other weakness (bug), an extra immunity against Normal, and no weaknesses Psychic has, plus the attacking type gets better coverage. The only benefit Psychic has over Ghost is that it resists Psychic, but Psychic is such an uncommon attacking type anyways...
But yeah, offensively, Psychic is only useful in two situations:
1) STAB without a secondary typing or with a complementary secondary Typing. So things like Alakazam and Azelf usually run Psychic for lack of another STAB option, and things like Gallade and Medicham often run Psychic because Psychic + Fighting hits everything except for other Psychics at least Neutral. But things like Metagross and Latias should never run Psychic, as thei secondary typings share many resists with Psychic (Steel, notably) and are better overall (Meteor Mash on meta due to power and Dragon Pulse on Lati due to neutral coverage).
2) As an NU/UU coverage move. There are only 6 Pokemon in OU with a Psychic or Fighting typing, one of those (lucario) is neutral to Psychic, and the rest of them are fairly uncommon save for Infernape. However, in NU/UU, there are a large number of Poison and Fighting types commonly used, including the Nidos, Hitmonlee and Hitmontop, Roserade, Crobat (assuming he gets out of Suspect without a ban), etc. In those formats, it is much more acceptable to use Psychic as a coverage move.