They have one way to approach the homeless problem and it is very involved: The homeless have to have an almost impossible set of things happen for them all at once or nothing whatever is done, instead of offering tools and partial solutions, sets of several options that they may be able to piece together into an overall solution. It's "all or nothing" with them. If a homeless person does not fulfill everything they get dropped from a program. Partial solutions might help people gradually put a life together and make it off the streets.
The cost vs benefits of such a program was prohitive. Most of the people that were asking for those welfare programs are either disables, either real or imagined. Single mothers also need free child care etc.etc.etc. The few that can't prove their disability are also unwilling to work. Most administration's have found it less of a burden to the taxpayers to just pay the entitlements and not be overly critical of the expected fraud. Just prosecute it when discovered. Locally, a case was successfully prosecuted against a woman who claimed to have cancer to get an abortion at government (Medicaid) expense.
Because it would expose the truth. That hundreds of thousands of white people have been displaced by open borders. It would end the myth of laziness and jobs they won't do.
There are guilt ridden well fed illegals that contribute to charities to help the people they've displaced. Interesting, don't you think? They just don't feel guilty enough to leave.