The homeless aren't prosecuted for sleeping outside. They're prosecuted for public indecency (i.e., exposing their privates to passersby and children), drug use, threats, physical violence, public intoxication.

The homeless advocates behind this lawsuit also assume that street life is somehow preferable to jail or prison, where occupants are provided 3 square meals a day, warm and clean clothing, a clean dedicated space to sleep, and all the free health services you need.

EDIT: Former public defender here. People have this bizarre, media-fueled image of jail and prison as horrible places to live. However, Oz is the minority of facilities--Orange is the New Black is far more representative of your typical incarceration facility. In many states, and especially on the West Coast, prison and jail facilities are nicer than the local schools. The only long-term homeless I've met that didn't want to go to jail--and in LA, I've encountered thousands of homeless individuals--were the drug addicts and drunks, because behind bars you're not allowed to drink or do drugs and they might give you medication that triggers withdrawal.