One of the benefits of institutionalizing the problematic homeless (either via incarceration or involuntarily mental health treatment, there's not a whole lot of difference between those two things from the perspective of the person subject to them anyway), is that it would allow the state to relax certain laws about simply being unsheltered without otherwise causing problems for people. Someone who is living silently and cleanly in their car is not a problem for me - I know more than one relatively well-paid, reasonably-intelligent person who is basically living that kind of lifestyle voluntarily - and I would prefer it if they weren't even getting a 15 minute knock from the cops once a month.