That brings up the question of what is "mentally ill"? In a criminal court, the prosecution will have five psychiatrists/psychologists saying the man is legally sane and the defense will have five psychiatrists/psychologists saying he's quite mad.
Because a person is mentally ill doesn't mean they can't modify or control their behavior. I knew quite a few people who were mentally ill and managed to control certain behaviors because they didn't like being in jail. It didn't make them well but it did make them less of a problem. An example was a schizophrenic who heard people talking about him, plotting against him, in darkened movie theaters. Sometimes he'd get so agitated he'd hit people. He'd go to the psych ward, promptly get released since he refused to take meds, and he'd go to a movie. When he went to jail instead and was told that every time he misbehaved in a movie theater he'd go to jail, he quit going to movies. He was still quite mad but wasn't punching people in the movie theater.
To say mentally ill people should go to the mental ward implies that something can be done for them there. We did have the man who was declared innocent of murder by reason of insanity that the state hospital wanted to release six weeks later because they determined he was quite normal but let's face it, that's crazy. In fact, very few spend their life in a mental hospital and even fewer get "cured".
A man called the police in Colorado Springs, Colorado, and said he needed to be arrested. He was killing people. His last name was Garrison. He was picked up and the police learned he'd been in a mental hospital in California for killing his mother and grandmother. They cured him and released him on furlough. He had to report back in for therapy which he did quite well. Eventually he met a panel of five doctors and was certified well. He laughed as he told the police that when the panel certified him well there was a woman's head in the trunk of his car in the parking lot.
Sometimes it makes you wonder who's crazy.
I wish it was cut and dried as people think. I wish psychiatrists and psychologists could really cure the mentally ill. I wish a court could order a mentally ill person to take their meds. I wish we were able to say who is and is not mentally ill. But, we can't.