As you pointed out: " there is a category of people who can be said to be in need of help, there are others who are quite within their right to do with their lives whatever they please". But, if you only provide help to those who need it and are willing to accept it, there would be no forced-treatment-problem like described. I am convinced that quite a few of the "homeless, mentally ill" would be willing to accept help, that they are usually denied (because of the lack of a house, job and insurance).
The problem with forced treatment is that while there is a category of people who can be said to be in need of help, there are others who are quite within their right to do with their lives whatever they please, as long as they are not explicitly breaking the law, but prefer non-conventional life choices.
The main problem with enforced norms is that it pigeonholes everyone into "standard acceptable human" categorization, and if you don't fit into it, you become an outlaw.
The western societies had great fun categorizing people into various abnormality groups, leading into practical eugenics (forced sterilizatin) and forced incarceration. See for example [0].
Germany's 1940's escapades brought this arbitrary categorization fad to an end with the holocaust, where it became explicitly clear what the logical end result is when you start mass categorizing people into first-grade and second-grade citizens.
I have close relatives who would have benefitted from forced treatment, but I still prefer a society that does not do this.
True, there is a difference between eugenics and declaring someone 'too sick', but not that great actually since we don't really have a reliable gauge for a persons mental health - hence, it becomes arbitrary categorization based on just not falling within subjective norms of the dominating culture within society.
[0] https://www.nature.com/scitable/forums/genetics-generation/a...