Obligation? No. A good idea? Yes. Support services are in cities, especially centers. Half of this comment page is full with "housing alone doesn't help, we need support structures for the people" - doesn't mix well with the "hey, let's just put all the undesirables on a bus and give them housing in the middle of nowhere".
The reality is that many of the visible homeless living in the city center are addicts, and they congregate in city centers, in part, because of cheap and easy access to drugs and like-minded people. In places like the Tenderloin in San Francisco, open drug use is everywhere you look now, and the city turns a blind eye to it.
Claiming that people need to remain in this environment to recover is extremely misguided.
Lower cost? That doesn't seem likely in a city like San Francisco, where the cost of real-estate, construction, labor is sky high and the housing supply is extremely limited.
Helping more people? In that sense, efficiency is meaningless if it's not efficacious. And all evidence suggests that social services in places like San Francisco and Seattle are not working well, despite the hundreds of millions of dollars spend each year.
As we've also seen, housing addicts in neighborhoods where open drug use and drug dealing is tolerated is not efficient. Yet that's exactly what happens in the Tenderloin today.
It's almost too stupid to be believed.
There's no way around this save by exclusion zones and forced concentration camps or prisons, each of which have their own exhorbitant externalities.