Those who can afford the legal costs should pursue such litigation if they think it's worth doing so. Organizations addressing homelessness are among the least able to afford such litigation. As someone who has donated to solve this problem, knowing that money is going to be wasted on litigation makes me less likely to support organizations who are going to waste it.
When I donated money last year to address this issue, I donated to an organization in Texas, despite living in San Francisco, because I knew the money was going to be wasted on the problem in San Francisco. When people making 6-figures right out of college have difficulty finding stable living arrangements in a place, it's futile to try and keep people in that same place that don't have nearly the same capacity to support themselves in an extraordinarily expensive market. For many homeless people, keeping them in SF is tantamount to keeping them homeless in perpetuity because almost none of them have a chance of escaping homelessness in that environment.