Psychiatrists charges have gradually increased over the years, as have those of other medical specialists, many of whom have increased even more. There is a degree of control over this, too, keeping them broadly in line. Doctors costs have gone up a lot, too. And have you tried hiring a plumber or long-distance taxi driver, or electrician lately ?
Government institutions can be rather hit and miss, but the psych facilities are not bad in this area, so far as I hear.
Its likely that the Tara Eating Disorders clinic can get overwhelmed if they tried to admit people self-diagnosed, so maybe they require a prior expert assessment and proper diagnosis by a psychiatrist at a state institution ( and I doubt they'd refuse one from a private specialist psychiatrist ).