I wonder if better/more accessible health care would eliminate homeless as a side effect. It seems much of the homeless in Boston, anyway is mental health/health related. I doubt anyone will say that what Utah did here is bad , but you have to wonder what's preventing a more comprehensive solution (the answer is politics, but ideally you'd get a more specific answer).
Here in Los Angeles the number of homeless who are severely mentally ill is incredibly high. It's quite common to see homeless people standing on street corners, yelling and screaming at non-existent antagonists, behaving bizarrely, urinating and defecating in broad daylight, and creating a general nuisance for everyone around them.
The same goes for seeing drug and alcohol use in public, especially in places like downtown LA and Venice Beach.
Seems to me that the homelessness isn't the problem, so much as a symptom of the underlying issues of addiction and mental illness, and unless people voluntarily seek treatment for those issues their situation is unlikely to change.
Whether the healthcare is available or not, the question is moot if you can't force people to go to rehab and take their meds.