They really don't. Trying to find a toilet you can use in downtown San Diego even as a regular looking person is a struggle and you will probably end up having to buy something. Businesses won't let you use their facilities if you look dirty or homeless, and there aren't any city owned bathrooms at least that I've seen in the 2 years I've been here so far.
Likewise in San Francisco. I like to take very long all-day or late night walks and bathrooms are very hard to come by. Sure as long as it’s daytime and I look presentable I can usually find a cafe/store that will let me use the bathroom, but after 9pm if I don’t happen to be near a hotel it’s often impossible for me to find a restroom. Many restaurants and convenience stores will say the bathroom is broken (even when it’s clearly not). Also it’s common to find places that physically block access to the restroom with boxes or whatever. Long story short, I’ve had to get used to peeing outside in shadows since it’s rarely possible to find bathrooms. I’m not sure what I’d do if I was female or needed to take a crap.
Fort Worth and Albuquerque give them jobs to clean up streets. In Fort Worth, they pay $10 per hour and provide housing. This would be similar - and a good idea, I think.