There's urine in the train stations (either visible or smellable), elevators shut down by faeces, people shouting, yelling and preaching in the streets, also, toilets, often even in private restaurants, are disgusting.
I don't mean to say that things are always like this, all the time or in all cities and I understand that it's a minority of people who cause these problems but the problems are far from uncommon.
With a place like a public bath in particular, cleanliness is extremely important and I just can't see it working. It only takes one inconsiderate person relieving them self in the water to ruin it for everyone and I find it hard to believe that in a day in an average US city you wouldn't find such a person. My impression is that it works in Japan because the society is extremely communal and you're far, far less likely to find such an inconsiderate person.
I can kind of see it working in smaller US communities where people know and respect each other though. In small communities, everyone knows each other and people are much less likely to be inconsiderate towards friends and acquaintances than they are towards strangers.