> Most people who enter homelessness leave it within a couple of weeks.

I'm a bit skeptical of the "Most" claim but it's based on anecdotal evidence from recent years of interacting with our sizable homeless community. I haven't seen any stats.

> They want to get back on their feet so they take advantage of social services

While the first part is undeniably true, the latter depends on the availability or existence of social services. Southern US states are openly hostile toward folks with long term vulnerabilities. Where services exist, politicians here proudly trim them back where they can.

>and maybe have broader support structure through friends and family.

My mom rescued me from homelessness when I was a teenager. The odds of escaping homelessness without help are ~0.