I have several friends who are homeless or who have been homeless. It's really difficult to overstate how hard it is to get back out of homelessness, once you reach that point, without significant outside help.
Think of all of the stuff most folks take for granted that are pretty much mandatory in most US cities in order to get and keep a job:
1. ID. So many of the homeless folks I know have had significant trouble obtaining ID after losing it or having it stolen, or having never had one because they left home at a very young age, etc. I can't count the number of conversations I've had trying to assist folks get an ID. Our governments don't make it easy (you need at least birth certificate and Social Security card, and some sort of mail showing where you live in some cases). For people without cooperative family or with no living parents, this step is very tough. It's stupid to think that lack of a tiny thing like ID is why so many people are without work and without homes, but, it's a reality.
2. Transportation. If you have no car in most US cities, it's hard to have a job. This one reason metropolitan areas are so much more densely populated by homeless folks; mass transit tends to be most accessible in the city center.
3. Staying clean. Would you hire someone who smells bad or looks dirty for any job? Homeless folks feel invisible because people don't want to be near dirty/smelly people of indeterminate mental health. Even if someone is perfectly able to do a job, being dirty is a guarantee they won't get the job.
4. No reliable way to reach them, if someone does decide to hire them. When I hear/see someone being hostile to a homeless or poor person because they are lucky enough to have a smart phone (I guess because a phone is an expensive thing), I'm just aghast. How the hell do they expect a homeless person to get out of homelessness without a phone, email, and a way to get online? So many low-level jobs have online application processes and require interaction via email and web in order to get the job.
5. Not getting a decent night's sleep, ever. Without a home, sleeping is a challenge every single day. If there are enough beds in the shelters (never the case in any city I've lived in), they have to be in the shelter by a certain time and have to be out very early (6AM is the "checkout time" at many shelters). This does double harm. The inflexible schedule prevents folks from holding jobs that conflict with that strict schedule, like second shift and night shift work, which often pays reasonably well, and has low barriers to entry. And, it also means they probably are running on an hour or two less sleep than a human actually needs to thrive. I hung out in downtown Eugene recently, and I was told that there was at least one fight, every single night. One broke out across the street within an hour of that conversation. I don't know that poor sleep is the cause of the frequent violence, but I'm confident it's a major contributing factor (and the science on sleep deprivation backs that theory up). Now, these were street kids, who don't go to shelters because the rules are too strict for them, and they sleep in sleeping bags and tents, but they, too, aren't getting enough sleep.
In short, having a home makes a huge difference in nearly every element of chronic poverty, and that, paired with a consistent income, are the things that most indicate whether someone will be able to become a self-sufficient functioning member of society again. This is a great idea, and it's awesome that Utah has had such great success with it. I hope more cities and states implement these ideas.