Which people? "Mentally ill" people aren't a homogenous group, and the fact that someone is mentally ill and living on the street does not imply that they are incompetent to make personal decisions due to their mental illness. The relation between mental illness, poverty, physical illness, etc. is complex.
There aren't simple answers, and this person isn't these people.
> If he was forcefully taken to the hospital, forcefully given medication, and recovered he would exclaim "Thank you for saving me! I had a disease in my brain that lead me to believe in crazy things: to be paranoid of police and even medical personnel. I spent 2 years on the streets suffering like this with no place I believed could help me, but you cured me."
Would he? He was medicated, functional from the point of view of the broader society, and living in an apartment and stopped taking his medication. Was it because the medication wasn't the best medical science could identify and he was still incompetent though he would be better off with other medication? Did he accidentally stop taking medication and start a downward spiral where he became out of control? Or was he, as he seemed, competent -- but voluntarily decided to discontinue the medication?
> If I had a mental disorder that made me go crazy--so crazy that it doesn't even enter my mind that I need help--I would hope that my government would restore my sanity (as I am unable to do so).
And that's great, but its a mistake to project what you think you would want onto other people as their preferences.