A cursory google search reveals that 1 in 4 of those in homeless shelters have a severe mental disorder. Nearly 1 in 2 have severe mental disorders and substance abuse problems.
These numbers do not paint a small minority that could benefit from institutionalization or other forms or long-term care, and our current system is poorly setup to handle these issues.
No, even local relocation (like forcing people into shelters for services) has been problematic historically.
> Many of these people need long term mental healthcare, and is the main reason they are homeless.
Yes, a minority do, and institutionalization (which, generally, might as well be outside of SF) may help a fraction of that minority.
Forced dislocation would also probably aggravate mental health problems for some others in (and out) of that that minority.
> Our current system is not well suited at helping people with mental disorders.
Sure, but “ship people elsewhere”, even if the responsibility doesn't shift, isn't a solution to that.