Also the motivations of the state are based on the motivations of any government. Buracracy is unavoidable.
If you're going to be handing out money, it would be better to give it to genuine charities that have an interest in helping the homeless. They generally will be better (imperfect of course, but better) at spending the money to help the most people.
The homeless oriented charities I'm aware of do amazing things with small amounts of resources, and they have to scrape by.
A real shame when we're blowing a $3.7 trillion dollar budget every year.