First, I agree with the general sentiment. However, there are some devilish details.
Take a look at some pictures of Gary, Indiana. It's an entire city that's been mostly abandoned since the collapse of the industry that built it. There are entire boarded up neighborhoods, and some quite fine large, brick houses where wealthy people used to live. It's all just sitting there. I'm sure that Gary would love to have people start moving back in, and revive the city.
So, say Gary just eminent-domained all those properties, and said to America: you want a house? All you have to do is come, pick one, and move in. You live in it for 5 years, it's your's.
The problem is that it costs money to keep up a home. Home maintenance is stupid expensive, and most of these abandoned homes need repairs: new windows, new roofs, new water heaters, plumbing repairs, electrical repairs. Do you have any idea what a new window costs? And even if it's sweat equity, and you're able to repair a roof yourself, you still need materials. Where does this money come from?
Are the homeless in California going to move to Gary, IN? Are the homeless in Alabama? There are homeless employed folks, but they're tied to their locations by their jobs. They're not moving to Gary.
Finally, it's a truism that it's often less expensive to tear down a house in poor condition and build a new one than it is to renovate. If these people don't have the money to build a new house, how are they going to afford to renovate a vacant one.
The problem is that people need jobs to live in a house (unless someone else is paying for taxes, insurance, and maintenance). And the places with jobs aren't the places like Gary, that have a abundance of empty homes. All of those empty homes are in inconvenient places, where the industry and jobs they created dried up.
It may be that a well-funded organization could artificially construct a self-sustaining community built on the bones of a dead one. But I think it's oversimplifying to suggest that you can just take an empty home away from the owner (let's assume you can) and just stick homeless people in it and assume it'll work - that, even given a house, they'll be able to afford to keep it heated, maintained, powered, insured. Shit, even if you given them a complete tax exemption, just keeping a house is expensive.
I'm sure there are some minority of homeless for whom giving an abandoned home in the area they live would solve their problems. And I'm sure that, for a while at least, having a bigger box to live in would be an improvement for many, even if the box is slowly falling apart around them. But I think it's naive to be angry about the number of empty homes, and that homelessness could be solved by relocating the homeless to where these places are and assigning them a house - whatever state it's in.