"Solve homelessness" doesn't mean no more homelessness and it's not a particular problem.

Homelessness is a consequence of many poor economic and social policies. I'll stick to a few of the economic ones.

Minimum wage: Often confused for a floor under wages, minimum wages are really a prohibition on pow productivity work. People who could justify modest wages of $6 or $7 an hour, and then potentially work their way up, are instead priced entirely out of the labor force. Also, city officials don't kick you off the street corner for earning less than minimum wage.

Occupational licensing: Almost every state has a bunch of ridiculously protected professions, that could otherwise be entry points into the labor force. Similar to minimum wage, if you make it harder to earn a living, fewer people will do so.

Building codes: It is illegal in many (probably most) places to build cheap housing, because bleeding heart do-gooders think all housing needs to be nice and full of amenities. Similar to minimum wages, making something harder to obtain reduces how many people are able to obtain it. Many people would pay to live in a simple apartment, that's little more than a bedroom, but it's illegal to build units that don't have kitchens and bathrooms, etc.

Public property: Ok, so in addition to making it harder to afford housing on several dimensions, cities also provide copious amounts of freely available space for anyone to use and still be close to all the city amenities.

We're essentially taxing a good (affordable housing) and subsidizing it's substitute (urban homelessness), so of course we have more than the socially optimal amount of urban homelessness.

This is why homelessness is highest in the cities with the worst economic policies.