People able to work should be required to work. Your plan does not allow for the people who are handicapped or mentally insane (which happen to be a very high percentage of the homeless). When a person can not differentiate a fork from a telephone... best of luck putting them to work.
Btw - we already provide food, heat and shelter for every convicted criminal (whether they work or not) and many have life sentences ... which run longer than most people stay on social assistance. So the message is, lets pay for people who damage our society... but not pay for people who simply lack aptitude but choose not to become criminals?