Solving the homeless problem is dead simple easy. The solution is to build more houses. Every apartment that gets built, is 1 less person being gentrified onto the streets.
The rooted people are the ones preventing developers from building more, because they don't want competition, and they want their housing prices to stay high.
Renters, are the ones getting screwed by this, because they have to pay the high rents that wouldn't exist without the artificially created barriers to entry.