It's not cheap even if you manage to get all your jails built in Sunset or some other backwater. Jail is expensive, and the homeless have no official salaries to garnish so you can't use the Ferguson method. Besides which, there's no way the state is going to take any convicted public poopers off your hands to house in their expensive prisons, so you're going to have to keep these criminals jailed for their entire sentence.
Wouldn't it be easier to open some public restrooms?