“The law, in its majestic equality, forbids rich and poor alike to sleep under bridges, to beg in the streets, and to steal their bread.” ― Anatole France
The cleverness of Anatole France's famous quote is that he framed it in a way that the answers to those questions were automatically obvious, by emphasizing the massive difference in agency and scope of action between the haves and the have nots.
I grew up in a very bad place in the UK and I knew many homeless people (different than homeless people in the US for sure, much lower propensity for mental health issues for example) but they avoided shelters because many homeless shelters aren’t safe. Any possessions you have will be stolen while you sleep. Women are molested and raped. Lice are all over. There are limited beds so giving up your "sure-fire" place in an underpass for a potential bed is not ideal.
You have to leave at 7 am and can’t return until 5pm at the earliest, and they’re first come first serve. Some shelters make you attend religious services.
Some shelters will "encourage" you to pay a fee to go to them.
It's very easy to become homeless and very difficult to get out of it (I mean, who has the finances to have 2 months rent, a deposit and enough to cover a failed background check), so it's not good to tar all homeless people with the "drug-use" brush.
I think you mean give them away exclusively to one group. The point of public services is to give them away.
Don't get me wrong. I think we should make massive investments in trying to solve the homeless problem, but giving away our public commons is utter stupidity.