Not really. I'm quite certain that arresting me for not carrying ID would be illegal in the United States. Note that in some states I might be required to identify myself, but simply stating my full name counts; I don't have to have a physical government-issued ID. Similarly, I am required to carry a driver's license when driving, but forgetting my license at home will at most result in a ticket.

There's just no plausible scenario where I get arrested and taken to jail simply for not having a physical ID with me.