What about the fact that, nation-wide, many Americans don't have access to good jobs? Especially people without college degrees, but not even limited to that. This is an economy-wide problem. The federal government could probably do something to better address that than a city government.
How about that we generally fail at mental health care, or health care in general? The former is clearly applicable to many homeless folks who are visibly suffering. The latter is a huge cost for many people, drives many personal bankruptcies, etc.
But I also place a lot of blame on state policies too - CA Prop 13 is a cancer on the whole state, incentivizing land owners to fight tooth and nail to prevent progress. I'm glad that Scott Wiener got elected, though, as he's been making solid progress at the state level to rectify these issues.
The roots of these problems are not broadly federal in my opinion and, while they certainly can help, there's a lot of work to do at the city and state level that are achievable with a small number of dedicated people - if only they cared.
Neither would I just blame the sorry state of US cities on inadequate mental health care - while healthcare broadly certainly should be better, I'm in Japan where mental health awareness is relatively speaking in the stone age compared to SF, and that hasn't resulted in the level of human tragedy you experience viscerally by existing for 5 minutes in any of the US's major metropolises. Part of the reason for that is I can get my own apartment without roommates 15 minutes from the center of Tokyo for $600/mo, largely because the local government here actually does things to make it livable (and it's not just here, it's practically everywhere besides US cities).
Allowing construction will alleviate pressure on the system as a whole, but, perhaps due to a failure of my imagination, I'm not seeing ways in which it won't cost something. I think it's worth it, mind you, I'm just not seeing how to make it $0.
In 2020 SF, even the upper middle class struggle to pay for housing. If you, as a first step, allow the housing stock to double, twice as many people can afford to live in the city, and life in SF becomes much more accessible.
Sure, there will always be people out of luck needing some assistance. But it should dwindle down to a smaller core when there are places to live.
Personally, I don't believe in government run housing. It's better to help people with rent money etc. But of course, none of this will ever happen in SF, so my opinions don't matter.