“Are people with mental problems more likely to go on a rampage if they are under the care of a psychiatrist/psychologist? They need to do a study on that.”
Shrink here: Studies of “the seriously mentally ill” - i.e. Schizophrenia and Bipolar Type I - show that they are no more likely than anyone else to become a danger to others . . . as long as . . . 1. They take their meds as prescribed, 2. They don’t use drugs or alcohol, and 3. They have no past history of violent behavior to others. That sub-set represents perhaps 10% of those living outside institutions . . . . It also cannot be extrapolated to other psych illnesses, such as this young man’s extreme narcissism.
To answer your question: No, I don’t think so. Most professionals do the best they can under the law to keep folks with mental illness from hurting themselves or others, but there’s really little they can do realistically in most cases in most jurisdictions. (The Tarasoff Ruling, BTW, put an unbelievable burden of protection on such professionals, a burden that is unprecedented in any other field, even law enforcement and the judicial system, as can be seen in this case and many others.)
I am sure that professionals do the best that they can. I see that you put several caveats in there. My question was not about the responsibilities of the professionals though it was simply about a statistical comparison of mass murderers who were under care vs. mass murderers who were not.