The police can only keep you for a limited time before you are given a trial before your peers where they have to present evidence of guilt, and you are sentenced to a limited time of incarceration.
A psychiatrist can keep you for an unlimited time, there is no appeal, no evidence besides their own judgement that you are “crazy”, and they can keep you until you are “cured” isolated in a padded cell drugged out of your mind.
As a father who has been court-appointed as my adult son's treatment guardian (diagnosed with Schizoaffectve Disorder), you're not exactly accurate. I have been through Mental Health court with my son and found it to be quite fair (maybe we were just lucky). By the way, we have two son's and one (who is not ill) is an AF pilot.
My ill son was appointed a lawyer and his rights were paramount in the mind of the judge. There were several doctors who provided testimony, along with myself as family. My son was court-ordered to be committed for 60 days, which at the time he really needed as he was suffering from severe psychosis. I'm happy to report that he is doing very well now and in fact just got promoted in the Civil Air Patrol - due to the right medications and treatment and an understanding family.
There is so much myth and misinformation about Mental Illness flying around that it is little wonder that those affected often don't accept treatment. For the record, I teach a 12-week course to family members who have loved ones diagnosed with serious brain disorders. In addition to teaching the course, I am also my state's coordinator for the NAMI Family-to-Family education program. I have taught this course probably 20 times to hundreds of family members since 2006, so feel I have more than average amount of insight into this subject. I'm sharing this because educating the public about the real nature of mental illness and the real need to recognize that illnesses like Schizophrenia, BiPolar, and Major Depression as the very real illnesses they are is important. I get very frustrated, for example, when the only time mental illness is discussed in the media, or by politicians, is on those rare, but terrible occasions when a mentally ill person does something tragic. The focus is always on gun-control, when the real problem is that, in most of these cases, there was a young man with a mental illness who wasn't getting the treatment he needed.
That is insightful... and sobering.