In the cases you cite, the way to deal with problem behavior usually involves medication, treatment, care, etc, but they still get to be participatory members of society.
The solution you're proposing would just lock them up in a high tower where the public could remain blissfully unaware that the mentally ill even exist, and never have to deal with them. I'd rather have to deal with somebody shitting on a bus once in a while than ostracize them and force them into a minimum security prison.
Standards are a guideline for how something should normally be. If someone is, by no fault of their own, radically outside this standard, they may require a separate standard to determine how they can be 'normal', and then find and receive treatment in order to live as close to normal as possible. Using the same standard for everyone would result in people being thrown into insane asylums for everything from anxiety to stress-induced nervous breakdown, bipolar disorder, OCD, schizophrenia, etc.
In 2012, there were an estimated 9.6 million adults aged 18 or older in the U.S. with a serious mental illness in the past year. This represented 4.1 percent of all U.S. adults. There were an estimated 43.7 million adults with any mental illness ; 18.6 percent of all U.S. adults. So yeah, I still don't think everyone should be held to the same standard, and I think treatment options should exist other than "hiding or banning from society".