I used to order them, I'm no longer able as the 2 ivory towers near me don't allow it anymore. I think the answer is very rarely in general psych and semi-rarely in neuropsych or liaison psych. EEG referrals from psychiatry have the lowest hit rate. However if you are thinking about frontal lobe seizures, temporal lobe seizures, non-convulsive status epilepticus, delirium/encephalopathy, then it is worth considering. Can be helpful in some cases in distinguishing dissociative disorders from encephalopathic or epileptic conditions, and in some cases in distinguishing functional cognitive disorders from coarse brain disease. I've actually had a few pts who were referred to me for anxiety who were actually having seizures. In one case the referral came from an epileptologist! of course, an EEG is not needed to dx seizures but can be helpful in some cases.
I can tell you that they can be helpful on C-L is assisting distinguishing delirium from primary psychiatric disorder. Makes it harder for the team to claim this is psych when the EEG shows triphasic waves (although they might still try!) The problem is the sensitivity of a spot EEG is not great for delirium, nor for epilepsy.