Letting people live on the streets is massively expensive for our country. Street people need huge amounts of medical care and police attention, which is not cheap. The most extreme examples of this end up receiving ICU care regularly throughout the year. ICU isn't cheap to run, not to mention that having regulars going through there repeatedly ties up beds and attention for normal cases.
I've read a lot of well done studies suggesting and even testing out the idea that its cheaper to just house the worst habitually at risk street people and task a full time squad of people to baby sit them than it is to pay their ICU bills all year.
So from just a pure money perspective, housing as a 'right' is going to save us money in the long run.
I've included this link to an LA Times article citing a Utah housing assistance program and how much it saves that city in medical expense.