The single best thing governments could do is increase density in areas with high economic opportunity. This can also be done very easily with a few strokes of the pen: Higher density zoning, and a land value tax.
Land value tax is critical as it ensures that landowners must develop their land rather than simply rent-seek if they are lucky enough to own in a desirable and growing area.
Interesting. Question: do you think that if all of a sudden a wand was waved and everyone homeless in a given city/geography was magically housed that there would still be (eventually, over time) further homelessness or do you think that homelessness would cease to exist from that point forward? What do you think would happen in say, 5-10-15 years out?
When a city is more hospitable to the homeless, it attracts more homeless. The homeless problem in California's major cities is in part due to their their (relatively) accommodating treatment of the homeless.
Cities, even states, aren't ever going to be able to fully tackle this problem alone - there needs to be a massive initiative at the federal level.
What would that look like to you?
Socialized housing is absolutely the answer, but homelessness will never be solved until we stop treating housing as an investment. Housing increasing in value is also housing increasing in cost. Investment growth is diametrically opposed to affordability.