No you don't. If I drive a car, I have to have license and show that if asked by the police but that is a requirement of driving. If I am a passenger, I don't have to have an ID. I can take an airplane flight without an ID, that has been shown time and time again. Taking the train and ID'ing yourself might be condition of being able to use a train, not law.
If I am out and about, I don't have to show the military my ID, I don't have to show security guards my ID and if I am not accused of a crime, I don't have to show the police my ID. Try that in China.
> To get a mobile phone you have to ID yourself (and sign in-person for the package if a phone is delivered to you) in the US.
Not true. I bought a T-Mobile SIM card with cash and activated it at home and I could have put anything into the address information. I have never once shown my ID when dealing with my T-Mobile account. Try doing that in China.