Prisoners cost ~ $40k a year annually in taxes. It's actually cheaper to house them - so I don't think states are going to be gung-ho about doing either.
Sending the poor to use expensive military kit on vulnerable foreign populations and arresting the non compliant is much more profitable than just providing every one of them with shelter and job opportunities. Society doesn't optimize globally for good will, it optimizes locally for profit.
San Jose CA has a homeless budget of approximately $120M per year. It has 500 beds. That's $240k/bed-year.
Of course, a lot of that $120M does NOT go to those beds, and there are some other facilities, but that $120M isn't all of the spending either.
The racket is that many prisions are private for-profit companies. So this is a way to funnel taxpayer money into those corporations. Who in turn are friends and campaign contributors of the politicians who push for more people into prisions. So it all feeds itself and the cost doesn't matter. The more cost, the better (to them).