I'm guessing both. I think a lot of people get the ick about forcibly incarcerating people who are addicts or suffering from severe mental health issues[1]. I know I did when I was younger. We've moved to a more voluntary model of "mental health outreach" and the like. But this requires folks with compromised thought processes to regularly make a rational decision to seek help.

[1] https://en.wikipedia.org/wiki/Deinstitutionalisation

There's a huge difference between "suffering from severe mental issues" (which is very hard to establish an objective standard for) and engaging in outright anti-social, criminal behavior. The latter can most certainly result in incarceration or court-ordered treatment, and no one sensible will "get the ick" about that.

There is also deindividuation which occurs in homelessness. You are rarely referred to by your own name and ignored or practically invisible by everyone else except by those providing services. I was homeless for 6 years so this was apparent in a lot of that society. In red states there was a third cohort: those disowned by families for having a differing view than them so they got kicked out. It takes a minimum of one year to recover from the effects of homelessness, mentally. That process only begins after they are rehoused.