I think you are overestimating the number of our homeless who match your accurate for some description. They aren't the chronic public inebriates and addicts, and self-medicating mentally ill, who are the majority of the clientele and source of the majority of the problems.

The people who spend their days on street corners begging simply because it is a low effort way to support the lifestyle that they have, unfortunately, accepted if not embraced. Anecdotally, even the still apparently physically able, if offered a cash job doing jobsite labor, will have a myriad of excuses, none of which are "I have nowhere to shower or do laundry."

A huge part of the problem remain well-meaning people who continue to falsely conflate the above population with the more sympathetic and photogenic minority who are temporarily in dire straits due to circumstances actually out of their direct control or who are actively seeking to better themselves. Practical solutions require honest assessments.