I do.
The harm is being done and the crime is being committed regardless of motivation, mental state, or ignorance of the law. Semantics can be argued all day, but the end result is a harm on society.
If criminal justice was actually about getting people the help they need rather than doing time, that'd be totally different.
What do you do in cases like that if prison is off the table?
I didn't watch the video mostly because I don't know what it contains and I have kids around. Making the assumption that it's about people who want to be homeless, honestly that's fine. There's nothing inherently wrong about being homeless if that's what you want. The problem is people causing public health issues because they defecate in public areas, tear apart trash bins, or cause other issues like attacking other people... none of which is acceptable to society. These people may not want to be part of society, but they are living where society exists.
The video explores the visibly-homeless issue in Seattle, as well as a program to address the problem that was implemented in Rhode Island (specifically, enforcement + long-term treatment). I found it worth the watch.
Only sometimes, and only for some crimes. It really is rather complicated. Legal philosophy recognizes that the primary purpose of punishments for crime is to deter people from committing crimes, and it therefore doesn't make sense to punish people who are too mentally ill to understand (a) what they were doing, or (b) that it was wrong, or (c) that they would be punished, or (d) what 'punishment' even is.
But legal philosophy is not a wasteland of common sense, and it's also recognized that one of the purposes of punishment for crimes is to prevent recurrence by making it impossible. The legal authority of the state to indefinitely imprison people who are dangerous to others through no fault of their own is well established.