Didn't a US city try that and confirm that you are correct? I mean, it's not just studies but also real world experience. Or to put it another way: the studies were studying real world interventions, for instance this one

https://www.ncbi.nlm.nih.gov/pubmed/10737824

examined a program that ran for five years with a high success rate.

There is a readable article on this at https://www.motherjones.com/politics/2015/02/housing-first-s...